Question

If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.

 

Answer 1

We know that 
\[\sin^{- 1} x + \cos^{- 1} x = \frac{\pi}{2}\].
We have
\[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2}\]
\[ \Rightarrow \sin^{- 1} \left( \frac{1}{3} \right) = \frac{\pi}{2} - \cos^{- 1} x\]
\[ \Rightarrow \sin^{- 1} \left( \frac{1}{3} \right) = \sin^{- 1} x\]
\[ \Rightarrow x = \frac{1}{3}\]
∴ \[x = \frac{1}{3}\]