Solve for x : sin^-1x - cos^-1x = π/6

Question

Solve for x :

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

Answer 1

Given: \(sin^{-1}x-cos^{-1}x=\frac{\pi}{6}\)

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

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

Substituting in the given equation,

Therefore, \(x=\frac{\sqrt{3}}{2}\)is the required value of x.