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

Solution:

Inverse trigonometric functions are the inverse ratio of the basic trigonometric ratios. 

Here the basic trigonometric function of Sin θ = y, can be changed to θ = sin^-1 y

Let, tan^{- 1} (1) = x

Hence,

cos x = 1/2

= cos (π / 3)

Therefore,

cos^{- 1} (1/2) = π / 3

Let, sin^{- 1} (1/2) = y

Hence,

sin y = 1/2

= sin (π / 6)

Therefore,

sin^{- 1} (1/2) = π / 6

Thus,

cos^{- 1}(1/2) + 2 sin^{- 1}(1/2)

= π / 3 + 2 (π / 6)

= 2 π / 3

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NCERT Solutions for Class 12 Maths - Chapter 2 Exercise 2.1 Question 12

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

Summary:

The value of cos^{- 1} (1/2) + 2sin^{- 1} (1/2) = 2 π / 3 . Inverse trigonometric functions are the inverse ratio of the basic trigonometric ratios