Question

If then value of the expression

sin^–1(cos(cos^–1(cosx) + sin^–1(sinx))) equals

• A. $- \frac { \pi } { 2 }$
• B. $\frac { \pi } { 2 }$
• C. 0
• D. None

Answer 1

Answer: (B)

$\frac { \pi } { 2 }$

Answer 2

Q cos^–1 cosx = cos^–1 cos(2p - x) for xĪ $\left( \frac { 3 \pi } { 2 } , 2 \pi \right)$= 2p - x

sin^–1 sinx = x – 2p

\ sin^–1 (cos (cos^–1(cosx) + sin^–1(sinx)))

= sin^–1 (cos 0) = sin^–1 (1) = $\frac { \pi } { 2 }$