If sin^-1 x + sin^-1 y = 2π/3 then (cos^-1 x + cos^-1 y) = ?

Question

If sin^-1 x + sin^-1 y = \(\frac{2\pi}{3}\) then (cos^-1 x + cos^-1 y) = ?

A. \(\frac{\pi}{6}\)

B. \(\frac{\pi}{3}\) 

C. \(\pi\)

D. \(\frac{2\pi}{3}\)

Answer 1

Correct Answer is (B) \(\frac{\pi}{3}\)

Given:  sin^-1 x + sin^-1 y = \(\frac{2\pi}{3}\) 

Since we know that sin^-1 x + cos^-1 x = \(\frac{\pi}{2}\)

⇒ cos^-1 x = \(\frac{\pi}{2}\)- sin^-1 x 

Similarly, cos^-1 y = \(\frac{\pi}{2}\)- sin^-1 y

Now consider cos^-1 x + cos^-1 y = \(\frac{\pi}{2}\)- sin^-1 x + \(\frac{\pi}{2}\) - sin^-1 y

= \(\frac{2\pi}{2}\) - [sin^-1 x + sin^-1 y]

= π - \(\frac{2\pi}{2}\)

= \(\frac{\pi}{3}\)