Evaluate sin⁻¹(cos(sin⁻¹ x)) + cos⁻¹(sin(cos⁻¹ x)) for valid x.
pi/2
pi
0
pi/4
Correct answer: pi/2
Solution
Let t = sqrt(1 - x²). Then cos(sin⁻¹ x) = t and sin(cos⁻¹ x) = t. So the expression is sin⁻¹(t) + cos⁻¹(t) = pi/2 (valid identity since t in [0,1]). Therefore the value is pi/2.