# NCERT Solutions for Class 12 Maths Inverse Trigonometry Functions Miscellaneous Exercise

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*NCERT Solutions** NCERT Solutions for Class 12 Maths* are not only the solutions of Maths exercise but it builds your foundation of other important subjects. Getting knowledge of depth concept of

*like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.*

**CBSE Class 12**^{th}Maths* CBSE Class 12^{th}* is an important school class in your life as you take some serious decision about your career. And out of all subjects, Maths is an important and core subjects. So

*is major role in your exam preparation as it has detailed chapter wise solutions for all exercise.*

**CBSE NCERT Solutions for Class 12**^{th}MathsAs we know that all the schools affiliated from CBSE follow the NCERT books for all subjects. You can check the **CBSE NCERT Syllabus**. Thus, * NCERT Solutions* helps the students to solve the exercise questions as given in

*.*

**NCERT Books**## NCERT Solutions for Class 12 Maths Inverse Trigonometry Functions Miscellaneous Exercise

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 1.**

Find the value of cos^{-1}(cos13π/6).

**NCERT Solutions:**

Given that cos^{-1}(cos13π/6).

We know that cos^{-1}(cosx) = x if the principle value of cos^{-1}x is x ∊ [0, π].

Since 13π/6 ∉ [0, π], we have

cos^{-1}(cos13π/6) = cos^{-1}(cos(2π + π/6)) = cos^{-1}(cos(π/6)).

Since π/6 ∊ [0, π], we have

cos^{-1}(cos13π/6) = cos^{-1}(cos(2π + π/6)) = cos^{-1}(cos(π/6)) = π/6.

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 2.**

Find the value of tan^{-1}(tan7π/6).

**NCERT Solutions:**

Given that tan^{-1}(tan7π/6).

We know that tan^{-1}(tanx) = x if the principle value of tan^{-1}x is x ∊ (-π/2, π/2).

Since 7π/6 ∉ (-π/2, π/2), we have

tan^{-1}(tan7π/6) = tan^{-1}(tan(π + π/6) = tan^{-1}(tan(π/6)).

Since π/6 ∊ (-π/2, π/2), we have

tan^{-1}(tan7π/6) = tan^{-1}(tan(π + π/6) = tan^{-1}(tan(π/6)) = π/6.

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 3.**

Prove that 2sin^{-1}(3/5) = tan^{-1}(24/7).

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 4.**

Prove that sin^{-1}(8/17) + sin^{-1}(3/5) = tan^{-1}(77/36).

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 5.**

Prove that cos^{-1}(4/5) + cos^{-1}(12/13) = cos^{-1}(33/65).

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 6.**

Prove that cos^{-1}(12/13) + sin^{-1}(3/5) = sin^{-1}(56/65).

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 7.**

Prove that tan^{-1}(63/16) = sin^{-1}(5/13) + cos^{-1}(3/5).

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 8.**

Prove that tan^{-1}(1/5) + tan^{-1}(1/7) + tan^{-1}(1/3) + tan^{-1}(1/8) = π/4.

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 9.**

Prove that tan^{-1}(√x) = (1/2)cos^{-1}((1 – x)/(1 + x)), x ∊ [0, 1].

**NCERT Solutions:**

LHS = tan^{-1}(√x) = (1/2)(2tan^{-1}(√x)) = (1/2)cos^{-1}((1 – x)/(1 + x)) = RHS

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 10.**

Prove that .

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 11.**

Prove that .

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 12.**

Prove that 9π/8 – (9/4)sin^{-1}(1/3) = (9/4)sin^{-1}(2√2 /3).

**NCERT Solutions:**

LHS = 9π/8 – (9/4)sin^{-1}(1/3) = (9/4)(π/2 – sin^{-1}(1/3)) = (9/4)(cos^{-1}(1/3)) = (9/4)sin^{-1}(2√2 /3) = RHS.

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 13.**

Solve the equation 2tan^{-1}(cos x) = tan^{-1}(2cosec x).

**NCERT Solutions:**

Given that

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 14.**

Solve the equation tan^{-1}((1 – x)/(1 + x)) = (1/2)tan^{-1}(x), x > 0.

**NCERT Solutions:**

Given that

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 15.**

sin(tan^{-1}x), |x| < 1 is equal to

**NCERT Solutions:**

Given that sin(tan-1x) = sin(sin-1(x/√(1 + x^{2}))) = x/√(1 + x^{2}). Correct option is D.

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 16.**

Solve the equation sin^{-1}(1 – x) – 2sin^{-1}(x) = π/2

(A) 0, 1/2 (B) 1, 1/2 (C) 0, (D) 1/2

**NCERT Solutions:**

Given that

Put x = sin y, then

Now, at x = 1/2, we have Thus

Thus, x = 1/2 is not a solution. Correct option is C.

**NCERT Solutions for Class 12 Maths Inverse Trigonometry Misc ****Exercise****: Ques No 17.**

tan^{-1}(x/y) – tan^{-1}((x – y)/(x + y)) is equal to

(A) π/2 (B) π/3 (C) π/4, (D) -3π/4

**NCERT Solutions:**

Given that

Correct option is C.