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Chapter 2 Inverse Trigonometric Functions Ex 2.2 Solutions

Question - 11 : - Find the value of 

Answer - 11 : -

Question - 12 : - Find the value of 

Answer - 12 : -

Question - 13 : - Find the value of 

Answer - 13 : -

Let x =tan θ. Then, θ = tan−1 x.

Let y =tan Φ. Then, Φ = tan−1 y.

Question - 14 : - If, then find the value of x.

Answer - 14 : -

On squaring both sides, we get:
Hence, the value of x is

Question - 15 : - If, then find the value of x.

Answer - 15 : -

Hence, the value of x is 

Question - 16 : - Find the values of 

Answer - 16 : -

We know that sin−1 (sin x)= x if, which is the principal valuebranch of sin−1x.
Here,
Now, 
can be written as:

Question - 17 : - Find the values of 

Answer - 17 : -

We know that tan−1 (tan x)= x if, which is the principal valuebranch of tan−1x.
Here,
Now, can be written as:

Question - 18 : - Find the values of 

Answer - 18 : - Let. 

Then,

Question - 19 : - Find the values of is equal to

Answer - 19 : - We know that cos−1 (cos x)= x if, which is the principal valuebranch of cos −1x.
Here,

Now, can be written as:

Question - 20 : - Find the values of is equal to

Answer - 20 : - Let. 

Then,
We know that the range of the principal value branchof
∴

The correct answer is D.

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