Question

How do you simplify `sin(pi/2-x)(secx-cosx)`?

Answer 1

`sin^2 x`

Explanation:

`P = sin (pi/2 - x)(sec x - cos x)`
`sin (pi/2 - x) = cos x` --> complementary arcs.
`(sec x - cos x) = 1/(cos x) - cos x = (1 - cos^2 x)/cos x`.
There for,
`P = (cos x)(1 - cos^2 x)/(cos x) = 1 - cos^2 x = sin^2 x`