Question

If x Î$\left( \frac{3\pi}{2},2\pi \right)$, then value of the expression sin^–1

(cos^–1 (cos x) + sin^–1(sin x))), is equal to

• A. –p/2
• B. p/2
• C. 0
• D. None of these

Answer 1

Answer: (C)

0

Answer 2

For x Î$\left( \frac{3\pi}{2},2\pi \right)$, cos^–1 (cos x)

= cos^–1 (cos (2p – (2p – x)))

= cos^–1 (cos (2p – x)) = 2p – x

and sin^–1 (sin x) = sin^–1 (sin (2p + (x – 2p)))

= x – 2p

̃ cos^–1 (cos x) + sin^–1 (sin x)

= (2p – x) + (x – 2p) = 0.

Therefore

sin^–1(cos(cos^–1(cos x) + sin^–1 (sin x))) = sin^–1 0 = 0