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

**Answer.**

**Question. **Using the principal values, evaluate the following :

**Answer.**

**Question. **Using principal values evaluate the following :

**Answer,**

**Question. **What is the principal value of

**Answer.**

**Question. **What is the principal value of

**Answer.**

**Question. **Find the principal value of

**Answer.**

**Question. **Find the value of

**Answer.**

**Question. **Using principal value, find the value of

**Answer.**

**Question.**

**Answer.**

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

**Question. **What is the principal value of

**Answer.**

** 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

**Answer.**

**Question. **Write the value of

**Answer.**

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

**Question. **Using principal values, write the value of

**Answer.**

**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

**Question. **Write the principal value of

**Answer.**

**Question. **Write the value of

**Answer.**

**Question. **Write the value of

**Answer.**

**Question. **Write the principal value of

**Answer.**

** Question. Write the principal value of tan^{–1} (√3 ) – cot^{–1}(–√3).** tan

Answer.

^{–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

**Question. **Evaluate :

**Answer.**

**Question.**

**Answer.**

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

Answer.

** Question. Write the principal value of cos^{–1}[cos(680º)].** cos

Answer.

^{–1}[cos (680°)]

= cos

^{–1}[cos (2 × 360 – 40)] [ ∴ cos (n × 360 – !) = cos]

= cos

^{–1}(cos 40°) = 40°

**Question. **Write the principal value of

**Answer.**

**Question. **Find the value of the following :

**Answer.**

**Question. **Prove that :

**Answer.**

**Question. **Prove the following :

**Answer.**

**Question. **Prove the following :

**Answer.** L.H.S.

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

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 :

**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

**Question. **Prove the following :

**Answer.**

**Question. **Prove the following :

**Answer.**

**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)

**Question. **Prove the following :

**Answer.**

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

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

**Question. **Prove the following :

**Answer.**

**Question. **Prove the following :

**Answer.**

** Question. Solve for x : tan^{–1} (x + 2) + tan^{–1} (x – 2) = tan^{–1} (8/79) x > 0.**tan

Answer.

^{–1}(x + 2) + tan

^{–1}(x – 2) = tan

^{–1}(8/79)

**Question.**

**Answer.**

**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)

**Question.**

**Answer.**

**Question. **Prove the following :

**Answer.** 1st method :

**Question. **Prove the following :

**Question. **Prove the following :

**Answer.**

**Question.**

**Answer.**

**Question.**

**Answer.** Ist method

**Question. **Solve for x :

**Answer.**

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

**Question. **Prove that

**Answer.**

**Question. **Prove the following :

**Answer.**

**Question.**

**Answer.**

**Question.**

**Answer.**

**Question. **Prove that :

**Answer.**

**Question. **Find the value of the following :

**Answer.**

**Question. **Solve the following equation :

**Answer.**

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

^{–1}(1 – x) – 2 sin

^{–1}x = π/2

**Question. **Prove that :

**Answer.**

**Question.**

**Answer.**

**Question.**

**Answer.**

**Question. **Solve for x :**tan ^{–1} x + 2 cot^{–1} x = 2π/3**

**Answer.**tan

^{–1}x + 2 cot

^{–1}x = 2π/3

**Question.**

**Answer.**

**Question. Prove the following :**

**Answer.**

**Question. **Prove that :

**Answer.**

**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