The value of sin-1 cos (sin-1x)+ cos-1 sin( cos-1x) is

Question

The value of sin-1 cos (sin-1x)+ cos-1 sin( cos-1x) is (A) 0 (B) (π/4) (C) (π/2) (D) π

Tardigrade Admin · Accepted Answer

sin-1 [ cos(sin-1x)] + cos-1[sin(cos-1x)] = sin-1[sin((π/2) -sin-1x)] + cos-1 [cos((π/2)-cos-1x)] = (π/2) -sin-1 x + (π/2)-cos-1x = π-(sin-1x +cos-1x) = π- (π/2) = (π/2)

Q. The value of $sin^{- 1} cos (s i n^{- 1} x) + cos^{- 1} sin (cos^{- 1} x)$ is

0

$\frac{π}{4}$

$\frac{π}{2}$

$π$

Q. The value of sin−1cos(sin−1x)+cos−1sin(cos−1x) is

0

4π​

2π​

π

sin−1[cos(sin−1x)]+cos−1[sin(cos−1x)] =sin−1[sin(2π​−sin−1x)]+cos−1[cos(2π​−cos−1x)] =2π​−sin−1x+2π​−cos−1x =π−(sin−1x+cos−1x) =π−2π​ =2π​

Q. The value of $sin^{- 1} cos (s i n^{- 1} x) + cos^{- 1} sin (cos^{- 1} x)$ is

$\frac{π}{4}$

$\frac{π}{2}$

$π$