# The value of $\cos(\sin^{-1}x+\cos^{-1}x),|x|\leq 1$ is _____________.

Toolbox:
• $$sin^{-1}x+cos^{-1}x=\large\frac{\pi}{2}$$
• $$cos\large\frac{\pi}{2}=0$$
Ans: 0

Using the above formula
$$cos(sin^{-1}x+cos^{-1}x)=cos\large\frac{\pi}{2}$$

$$\Rightarrow\:cos\large\frac{\pi}{2}=0$$

edited Mar 16, 2013