Question

Find the value of  cos ( cos⁻¹ (√2/2) − π /2) ?

Answer 1

First recall that cos( x - π/2) = sin x,

So here, we're truly being asked to find

from the definition of an inverse function.

Keeping in mind that the domain of the inverse cosine is  [-1, 1], the only solution to the above equation is

x = π/4

Thus we get

sin (π/4) = √2/2