Question

If $\sin ({\sin }^{-1}\frac{1}{5}+{\cos }^{-1}x)=1$, then find the value of x

• A. $-\frac{1}{5}$
• B. $+\frac{1}{5}$
• C. $\pm \frac{1}{5}$
• D. None of these

Answer 1

Answer: (B)

$+\frac{1}{5}$

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