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Chapter 2 Inverse Trigonometric Functions Ex 2.1 Solutions

Question - 1 : -

Find the principalvalue of 

Answer - 1 : - Let sin-1 

Then sin y = 

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

and sin

Therefore, the principal value of 

Question - 2 : - Find the principal value of 

Answer - 2 : -

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

Therefore, the principal value of

Question - 3 : -

Find the principal value ofcosec−1 (2)

Answer - 3 : - Let cosec−1 (2)= y. Then, 

We know that the range of the principal value branchof cosec−1 is 
Therefore, the principal value of 

Question - 4 : - Find the principal value of 

Answer - 4 : -

We know that the range of the principal value branchof tan−1 is 
Therefore, the principal value of 

Question - 5 : - Find the principal value of 

Answer - 5 : -

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

Therefore, the principal value of 

Question - 6 : -

Find the principal value oftan−1 (−1)

Answer - 6 : - Let tan−1 (−1)= y. Then, 

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

Therefore, the principal value of 

Question - 7 : - Find the principal value of 

Answer - 7 : -

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

Therefore, the principal value of 


Question - 8 : - Find the principal value of 

Answer - 8 : -

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

Therefore, the principal value of 

Question - 9 : - Find the principal value of 

Answer - 9 : -

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

Therefore, the principal value of 

Question - 10 : - Find the principal value of 

Answer - 10 : -

We know that the range of the principal value branchof cosec−1 is 
Therefore, the principal value of 

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