Question

Find the integrals of the functions.
$\int si{n}^{-1}\left(cosx\right)dx.$

Answer 1

$\int si{n}^{-1}\left(cosx\right)dx=\int \{\frac{\pi }{2}-co{s}^{-1}(cosx\left)\right\}dx(\because si{n}^{-1}t+co{s}^{-1}t=\frac{\pi }{2}for|t|\le 1)=\int (\frac{\pi }{2}-x)dx=\frac{\pi }{2}x-\frac{x^2}{2}+C$