Question

If 4 sin⁻¹ x + cos⁻¹ x = π, then what is the value of x?

Answer 1

We know that
\[\sin^{- 1} x + \cos^{- 1} x = \frac{\pi}{2}\]
\[\therefore 4 \sin^{- 1} x + \cos^{- 1} x = \pi\]
\[ \Rightarrow 4 \sin^{- 1} x + \frac{\pi}{2} - \sin^{- 1} x = \pi \left[ \because \sin^{- 1} x + \cos^{- 1} x = \frac{\pi}{2} \right]\]
\[ \Rightarrow 3 \sin^{- 1} x = \frac{\pi}{2}\]
\[ \Rightarrow \sin^{- 1} x = \frac{\pi}{6}\]
\[ \Rightarrow x = \sin\frac{\pi}{6}\]
\[ \Rightarrow x = \frac{1}{2}\]
∴ \[x = \frac{1}{2}\]