Question

write the value of cos^-1 (-1/2)+2sin^-1 (1/2)

Answer 1

cos⁻¹ (-1/2) = 120 degrees sin⁻¹(1/2) = 30 degrees 
Therefore, cos^-1 (-1/2)+2sin^-1 (1/2) = 120 + 2(30) = 180 degrees 

Answer 2

${ \cos }^{ - 1} ( - \frac{1}{2} ) = \frac{2\pi}{3} or \: \frac{5\pi}{3}$
${ \sin }^{ - 1} ( \frac{1}{2} ) = \frac{\pi}{6} or \: \frac{5\pi}{6}$
So there will be 4 solutions
The first will be
$\frac{2\pi}{3} + \frac{2\pi}{6} = \pi$
The second will be
$\frac{5\pi}{3} + \frac{2\pi}{6} = 2\pi$
The third will be
$\frac{2\pi}{3} + \frac{5\pi}{3} = \frac{7\pi}{3}$
The fourth will be
$\frac{5\pi}{3} + \frac{5\pi}{3} = \frac{10\pi}{3}$