Question

If ${\sin }^{-1}\frac{x}{5}+{cosec}^{-1}\frac{5}{4}=\frac{\pi }{2}$, then $x$ is equal to:

• A. 1
• B. 4
• C. 3
• D. 5

Answer 1

Answer: (C)

3

${\sin }^{-1}\frac{x}{5}+{cosec}^{-1}\frac{5}{4}=\frac{\pi }{2}$

$\Rightarrow {\sin }^{-1}\frac{x}{5}+{\sin }^{-1}\frac{4}{5}=\frac{\pi }{2}$

$\Rightarrow {\sin }^{-1}\frac{x}{5}=\frac{\pi }{2}-{\sin }^{-1}\frac{4}{5}={\cos }^{-1}\frac{4}{5}$

$\Rightarrow x=5\sin {\cos }^{-1}\frac{4}{5}=5\sin {\sin }^{-1}\frac{3}{5}=3$