If ^-1x5+cosec^-154=2, then the value of x is

Question

If $\sin^{-1}\dfrac{x}{5}+	ext{cosec}^{-1}\dfrac54=\dfrac{\pi}{2}$, then the value of $x$ is

Accepted Answer

$$\sin^{-1}\frac{x}{5}=\frac{\pi}{2}-\text{cosec}^{-1}\frac54=\frac{\pi}{2}-\sin^{-1}\frac45=\cos^{-1}\frac45=\sin^{-1}\sqrt{1-\frac{16}{25}}=\sin^{-1}\frac35.$$

$$\frac{x}{5}=\frac35\ \Rightarrow\ x=3.$$

Solutions · 1