Question

Find the value of x if,

$sin\{{sin}^{-1}\frac{1}{5}+{cos}^{-1}x\}=1$

Answer 1

$\sin \{{\sin }^{-1}\frac{1}{5}+{\cos }^{-1}x\}=1$

$\Rightarrow {\sin }^{-1}\frac{1}{5}+{\cos }^{-1}x={\sin }^{-1}1$

$\Rightarrow {\sin }^{-1}\frac{1}{5}+{\cos }^{-1}x=\frac{\pi }{2}$

$\Rightarrow {\sin }^{-1}\frac{1}{5}=\frac{\pi }{2}-{\cos }^{-1}x$

We know that ${\sin }^{-1}x+{\cos }^{-1}x=\frac{\pi }{2}$

$\Rightarrow {\sin }^{-1}\frac{1}{5}={\sin }^{-1}x$

$\therefore x=\frac{1}{5}$