The value of cosec(sin⁻¹(-1/2)) - sec(cos⁻¹(-1/2)) is equal to:

The value of $\operatorname{cosec}\left(\sin^{-1}\left(-\frac{1}{2}\right)\right) - \sec\left(\cos^{-1}\left(-\frac{1}{2}\right)\right)$ is equal to:

(a)$-4$
(b)$0$
(c)$-1$
(d)$4$

Answer

Correct option: (b)

Answer: (b) $0$ $\sin^{-1}\left(-\frac12\right) = -\frac{\pi}{6}$, so $\operatorname{cosec}\left(-\frac{\pi}{6}\right) = -2$. $\cos^{-1}\left(-\frac12\right) = \frac{2\pi}{3}$, so $\sec\frac{2\pi}{3} = -2$. Hence the value is $-2 - (-2) = 0$.