# NCERT Solutions for Class 12 Maths Inverse Trigonometry Functions

Hi Students, Welcome to **Amans Maths Blogs (AMB)**. In this post, you will get the * NCERT Solutions for Class 12 Maths Inverse Trigonometry Exercise 2.2*. This

**can be downloaded in PDF file. The downloading link is given at last.**

*NCERT Solutions** 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* 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## NCERT Solutions for Class 12 Maths Inverse Trigonometry Functions Exercise 2.2

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 1.**

Prove that 3sin^{-1}x = sin^{-1}(3x – 4x^{3}), where x ∈ [-1/2, 1/2]

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 2.**

Prove that 3cos^{-1}x = cos^{-1}(4x^{3} – 3x), where x ∈ [1/2, 1]

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 3.**

Prove that tan^{-1}(2/11) + tan^{-1}(7/24) = tan^{-1}(1/2).

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**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 4.**

Prove that 2tan^{-1}(1/2) + tan^{-1}(1/7) = tan^{-1}(31/17).

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 5.**

Write the function tan^{-1}(√(1 + x^{2}) – 1)/x, x ≠ 0 in simplest form.

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 5.**

Write the function tan^{-1}(√(1 + x^{2}) – 1)/x, x ≠ 0 in simplest form.

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**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 6.**

Write the function tan^{-1}(1/√(x^{2} – 1)), |x| > 1 in simplest form.

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 7.**

Write the function tan^{-1}√((1 – cos x)/(1 + cos x)), x < π in simplest form.

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**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 8.**

Write the function tan^{-1}((cos x – sin x)/(cos x + sin x)), x < π in simplest form.

**NCERT Solutions:**

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 9.**

Write the function tan^{-1}(x/√(a^{2} – x^{2})), |x| < a in simplest form.

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**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 10.**

Write the function in simplest form.

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**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 11.**

Find the value of tan^{-1}(2cos(2sin^{-1}(1/2))).

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**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 12.**

Find the value of cot(tan^{-1}(a) + cot^{-1}(a)).

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**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 13.**

Find the value of .

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**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 14.**

If sin(sin^{-1} 1/5 + cos^{-1} x) = 1, then find the value of x.

**NCERT Solutions:**

Given that sin(sin^{-1} 1/5 + cos^{-1} x) = 1.

Since sin(A + B) = sinAcosB + cosAsinB, we have

On squaring both sides, we get

⇒ 4[6(1 – x^{2})] = 25 + x^{2} – 10x

⇒ 24 – 24x^{2} = 25 + x^{2} – 10x

⇒ 25x^{2} – 10x + 1 = 0

⇒ (5x – 1)^{2} = 0

⇒ 5x – 1 = 0

⇒ x = 1/5

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 15.**

If tan^{-1}((x – 1)/(x + 2)) + tan^{-1}((x + 1)/(x + 2)) = π/4, then find the value of x.

**NCERT Solutions:**

Given that tan^{-1}((x – 1)/(x + 2)) + tan^{-1}((x + 1)/(x + 2)) = π/4.

Since tan^{-1}x + tan^{-1}y = tan^{-1}(x + y)/(1 – xy), we have

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 16.**

Find the value of sin^{-1}(sin2π/3).

**NCERT Solutions:**

Given that sin^{-1}(2π/3).

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

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 17.**

Find the value of tan^{-1}(tan 3π/4).

**NCERT Solutions:**

Given that tan^{-1}(tan 3π/4).

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

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 18.**

Find the value of tan(sin^{-1} 3/5 + cot^{-1} 3/2).

**NCERT Solutions:**

Given that tan(sin^{-1} 3/5 + cot^{-1} 3/2).

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 19.**

Find the value of cos^{-1}(cos 7π/4).

(A) 7π/6 (B) 5π/6 (C) π/3 (D) π/6

**NCERT Solutions:**

Given that cos^{-1}(cos^{-1} 7π/4).

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

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 20.**

Find the value of sin(π/3 – sin^{-1}(-1/2)).

(A) 1/2 (B) 1/2 (C) 1/4 (D) 1

**NCERT Solutions:**

Given that sin(π/3 – sin^{-1}(-1/2)).

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

**NCERT Solutions for Class 12 Maths Inverse Trigonometry ****Exercise**** 2.2: Ques No 21.**

Find the value of tan^{-1}√3 – cot^{-1 }(-√3).

(A) π (B) -π/2 (C) 0 (D) 2√3

**NCERT Solutions:**