Question

51 1. cos-1 {-sin(5π/6)} is equal to
a.-5π/6
b.5π/6
c.2π/3
d.-2π/3​

Answer 1

Answer:

The correct answer is option (c) .

Step-by-step explanation:

$\cos^{-1}(-\sin\frac{5\pi}{6})=\cos^{-1}(-\sin(\pi-\frac{\pi}{6}))$

                        $=\cos^{-1}(-\sin\frac{\pi}{6})$, since $\sin(\pi-\theta)=\sin\theta$

                        $=\cos^{-1}(-\frac{1}{2})\\=\frac{2\pi}{3}$

• (Since range of $\cos^{-1}x$ is $[0,\pi]$ and $\cos\frac{2\pi}{3}=-\frac{1}{2}$ )