Simplify the Problem

Question

cos(pi/2 - x)[sec(pi/2 - x)-cos(pi/2 - x)]

Answer 1

cos(pi/2 - x)[sec(pi/2 - x)-cos(pi/2 - x)]

temporarily replace (pi/2 - x) with A

cosA * secA - cos² A = 1 - cos² A

At this point, recall that cos²X + sin²X = 1

So, we have sin²(pi/2 - x)

Finally, note that sin(pi/2 - x ) = cos(x)

Answer 2

cos (π/2 - θ)[sec (π/2 -θ) - cos (π/2 - θ)]

sin θ [ (1 / cos (π/2 - θ)) - sin θ]

sin θ [ (1/ sin θ) - sin θ]

1 - sin² θ

cos² θ

Look up a table of the frequent convesions.