Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Students can read the important questions given below for Inverse Trigonometric Functions Class 12 Mathematics. All Inverse Trigonometric Functions Class 12 Notes and questions with solutions have been prepared based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS. You should read all notes provided by us and Class 12 Mathematics Important Questions provided for all chapters to get better marks in examinations. Mathematics Question Bank Class 12 is available on our website for free download in PDF.

Important Questions of Inverse Trigonometric Functions Class 12

Short Answer Type Questions

Question. Write the principal value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Using the principal values, evaluate the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Using principal values evaluate the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer,

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. What is the principal value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. What is the principal value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Find the principal value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Find the value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Using principal value, find the value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. If sec–1(2) + cosec–1(y) = π/2, then find y.
Answer. sec– 1 (2) + cosec – 1 y = π/2

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. What is the principal value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Write the principal value of tan–1 (– 1). (Foreign)
Answer. tan–1 (– 1)
= – tan–1 (1)                              [tan–1 (– !) = – tan–1 !]
= – tan–1 (tan π/4) = –π/4

Question. Write the value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Write the value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Find the principal value of tan–1 √3 – sec–1 (– 2).
Answer. tan–1 (3 ) – sec–1 (– 2)

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Using principal values, write the value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. If tan–1 x + tan–1 y = π/4, where xy < 1, find the value of x + y + xy.
Answer. tan–1 x + tan–1 y = π/4

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Write the principal value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Write the value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Write the value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Write the principal value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Write the principal value of tan–1 (√3 ) – cot–1(–√3).
Answer.
tan–1 (√3 ) – cot–1(–√3)
= tan–1√3 – (π – cot–1√3)
( ∴ cot–1 (– !) = π – cot–1 π)
= tan–1 √3 + cot–1 √3 – π

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Evaluate :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. If tan–1 x + tan–1 y = π/4, xy < 1, then write the value of x + y + xy.
Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Write the principal value of cos–1[cos(680º)].
Answer.
cos–1 [cos (680°)]
= cos–1 [cos (2 × 360 – 40)]                              [ ∴ cos (n × 360 – !) = cos]
= cos–1 (cos 40°) = 40°

Question. Write the principal value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Find the value of the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove that :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer. L.H.S.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve for x : tan–1 3x + tan–1 2x = π/4
Answer. tan–1(2x) + tan–1(3x) = π/4

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Rejecting x = – 1, it not does satisfy the equation as the L.H.S. of (i) is –ve. and R.H.S. of (i) is +ve Hence x = 1/6

Question. Solve the following for x :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve the following for x : tan–1 x + 2 cot–1 x = 2π/3
Answer. tan–1 x + 2 cot–1 x = 2π/3

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove that : tan–1 (1) + tan–1 (2) + tan–1 (3) = π.
Answer. L.H.S. = tan–1 (1) + tan–1 (2) + tan–1 (3)

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove the following : cos [tan–1 {sin(cot–1 x)}]

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer. L.H.S. = cos[tan–1 {sin(cot–1 x)}]

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve for x : tan–1 (x + 2) + tan–1 (x – 2) = tan–1 (8/79) x > 0.
Answer. 
tan–1 (x + 2) + tan–1 (x – 2) = tan–1 (8/79)

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve for x : 2 tan–1 (sin x) = tan–1(2 sec x)
Answer. 2 tan–1(sin x) = tan–1(2 sec x)

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer. 1st method :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer. Ist method

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve for x :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve for x : cos(2 sin–1 x) = 1/9, x > 0
Answer. cos(2 sin–1 x) = 1/9

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove that

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove that :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Find the value of the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve the following equation :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve for x :
sin–1 (1 – x) – 2 sin–1 x = π/2
Answer.
sin–1 (1 – x) – 2 sin–1 x = π/2

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove that :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve for x :
tan–1 x + 2 cot–1 x = 2π/3
Answer. tan–1 x + 2 cot–1 x = 2π/3

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove that :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. If sin[cot–1 (x + 1)] = cos(tan–1 x), then find x.
Answer. sin[cot–1 (x + 1)] = cos(tan–1 x)
⇒ sin A = cos B

Inverse Trigonometric Functions Class 12 Mathematics Important Questions