NCERT Solutions for Class 12 Science Math Chapter 2 Inverse Trigonometric Functions are provided here with simple step-by-step explanations. These solutions for Inverse Trigonometric Functions are extremely popular among Class 12 Science students for Math Inverse Trigonometric Functions Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the NCERT Book of Class 12 Science Math Chapter 2 are provided here for you for free. You will also love the ad-free experience on Meritnation’s NCERT Solutions. All NCERT Solutions for class Class 12 Science Math are prepared by experts and are 100% accurate.

Page No 41:

Question 1:

Find the principal value of

Answer:

Let sin-1 Then sin y =

We know that the range of the principal value branch of sin−1 is

and sin

Therefore, the principal value of

Page No 41:

Question 2:

Find the principal value of

Answer:

We know that the range of the principal value branch of cos−1 is

.

Therefore, the principal value of.

Page No 41:

Question 3:

Find the principal value of cosec−1 (2)

Answer:

Let cosec−1 (2) = y. Then,

We know that the range of the principal value branch of cosec−1 is

Therefore, the principal value of

Page No 41:

Question 4:

Find the principal value of

Answer:

We know that the range of the principal value branch of tan−1 is

Therefore, the principal value of

Page No 41:

Question 5:

Find the principal value of

Answer:

We know that the range of the principal value branch of cos−1 is

Therefore, the principal value of

Page No 41:

Question 6:

Find the principal value of tan−1 (−1)

Answer:

Let tan−1 (−1) = y. Then,

We know that the range of the principal value branch of tan−1 is

Therefore, the principal value of



Page No 42:

Question 7:

Find the principal value of

Answer:

We know that the range of the principal value branch of sec−1 is

Therefore, the principal value of

Page No 42:

Question 8:

Find the principal value of

Answer:

We know that the range of the principal value branch of cot−1 is (0,π) and

Therefore, the principal value of

Page No 42:

Question 9:

Find the principal value of

Answer:

We know that the range of the principal value branch of cos−1 is [0,π] and

.

Therefore, the principal value of

Page No 42:

Question 10:

Find the principal value of

Answer:

We know that the range of the principal value branch of cosec−1 is

Therefore, the principal value of

Page No 42:

Question 11:

Find the value of

Answer:

Page No 42:

Question 12:

Find the value of

Answer:

Page No 42:

Question 13:

Find the value of if sin−1x = y, then

(A) (B)

(C) (D)

Answer:

It is given that sin−1x = y.

We know that the range of the principal value branch of sin−1 is

Therefore,.

Page No 42:

Question 14:

Find the value of is equal to

(A) π (B) (C) (D)

Answer:



Page No 47:

Question 1:

Prove

Answer:

To prove:

Let x = sinθ. Then,

We have,

R.H.S. =

= 3θ

= L.H.S.

Page No 47:

Question 2:

Prove

Answer:

To prove:

Let x = cosθ. Then, cos−1x =θ.

We have,

Page No 47:

Question 3:

Prove

Answer:

To prove:

Page No 47:

Question 4:

Prove

Answer:

To prove:

Page No 47:

Question 5:

Write the function in the simplest form:

Answer:

Page No 47:

Question 6:

Write the function in the simplest form:

Answer:

Put x = cosec θθ = cosec−1x

Page No 47:

Question 7:

Write the function in the simplest form:

Answer:

Page No 47:

Question 8:

Write the function in the simplest form:

Answer:

tan-1cosx-sinxcosx+sinx=tan-11-sinxcosx1+sinxcosx=tan-11-tanx1+tanx=tan-11-tan-1tanx        tan-1x-y1+xy=tan-1x-tan-1y=π4-x



Page No 48:

Question 9:

Write the function in the simplest form:

Answer:

Page No 48:

Question 10:

Write the function in the simplest form:

Answer:

Page No 48:

Question 11:

Find the value of

Answer:

Let. Then,

Page No 48:

Question 12:

Find the value of

Answer:

Page No 48:

Question 13:

Find the value of

Answer:

Let x = tan θ. Then, θ = tan−1x.

Let y = tan Φ. Then, Φ = tan−1y.

Page No 48:

Question 14:

If, then find the value of x.

Answer:

On squaring both sides, we get:

Hence, the value of x is

Page No 48:

Question 15:

If, then find the value of x.

Answer:

Hence, the value of x is

Page No 48:

Question 16:

Find the values of

Answer:

We know that sin−1 (sin x) = x if, which is the principal value branch of sin−1x.

Here,

Now, can be written as:

Page No 48:

Question 17:

Find the values of

Answer:

We know that tan−1 (tan x) = x if, which is the principal value branch of tan−1x.

Here,

Now, can be written as:

Page No 48:

Question 18:

Find the values of

Answer:

Let. Then,

Page No 48:

Question 19:

Find the values of is equal to

(A) (B) (C) (D)

Answer:

We know that cos−1 (cos x) = x if, which is the principal value branch of cos −1x.

Here,

Now, can be written as:


cos-1cos7π6 = cos-1cosπ+π6cos-1cos7π6 = cos-1- cosπ6             as, cosπ+θ = - cos θcos-1cos7π6  = cos-1- cosπ-5π6cos-1cos7π6 = cos-1-- cos 5π6   as, cosπ-θ = - cos θ

The correct answer is B.

Page No 48:

Question 20:

Find the values of is equal to

(A) (B) (C) (D) 1

Answer:

Let. Then,

We know that the range of the principal value branch of.

The correct answer is D.

Page No 48:

Question 21:

Find the values of is equal to

(A) π (B) (C) 0 (D)

Answer:

Let. Then,

We know that the range of the principal value branch of

Let.

The range of the principal value branch of

The correct answer is B.



Page No 51:

Question 1:

Find the value of

Answer:

We know that cos−1 (cos x) = x if, which is the principal value branch of cos −1x.

Here,

Now, can be written as:

Page No 51:

Question 2:

Find the value of

Answer:

We know that tan−1 (tan x) = x if, which is the principal value branch of tan −1x.

Here,

Now, can be written as:

Page No 51:

Question 3:

Prove

Answer:

Now, we have:

Page No 51:

Question 4:

Prove

Answer:

Now, we have:

Page No 51:

Question 5:

Prove

Answer:

Now, we will prove that:

Page No 51:

Question 6:

Prove

Answer:

Now, we have:

Page No 51:

Question 7:

Prove

Answer:

Using (1) and (2), we have

Page No 51:

Question 8:

Prove

Answer:



Page No 52:

Question 9:

Prove

Answer:

Page No 52:

Question 10:

Prove

Answer:

Page No 52:

Question 11:

Prove [Hint: putx = cos 2θ]

Answer:

Page No 52:

Question 12:

Prove

Answer:

Page No 52:

Question 13:

Solve

Answer:

Page No 52:

Question 14:

Solve

Answer:

Page No 52:

Question 15:

Solveis equal to

(A) (B) (C) (D)

Answer:

Let tan−1x = y. Then,

The correct answer is D.

Page No 52:

Question 16:

Solve, then x is equal to

(A) (B) (C) 0 (D)

Answer:

Therefore, from equation (1), we have

Put x = sin y. Then, we have:

But, when, it can be observed that:

is not the solution of the given equation.

Thus, x = 0.

Hence, the correct answer is C.

Page No 52:

Question 17:

Solveis equal to

(A) (B). (C) (D)

Answer:

Hence, the correct answer is C.



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