Correct answer: sin(sin⁻¹ x) = x for x in [-1, 1]
For inverse trig functions, the identity f(f⁻¹(x)) = x holds whenever x lies in the domain of f⁻¹. Since sin⁻¹ x is defined for x in [-1, 1] and its output is an angle whose sine returns x, sin(sin⁻¹ x) = x for all x in [-1, 1]. The other statements are false: sin⁻¹(sin x) = x only for x in [-pi/2, pi/2]; cos(cos⁻¹ x) = x only for x in [-1, 1]; tan(tan⁻¹ x) = x for all real x.