Solve: sin⁻¹(cos(sin⁻¹ x)) = π/3

$\sin^{-1}(\cos(\sin^{-1}x)) = \frac{\pi}{3}$ $\cos(\sin^{-1}x) = \sin\frac{\pi}{3} = \frac{\sqrt{3}}{2}$ Let $\sin^{-1}x = \theta$; then $\cos\theta = \sqrt{1-x^2} = \frac{\sqrt{3}}{2}$ $1 - x^2 = \frac{3}{4}$, so $x^2 = \frac{1}{4}$ Hence $x = \pm\frac{1}{2}$.