cosx(secx-cosx)=sin^2x

Question

prove the following identities:

Answer 1

Recall the trigonometric identities

1/secx = cosx, cos^2x+sin^2x = 1

Left hand side = cosx(secx-cosx)

= cosxsecx-cos^2x

= cosx*1/cosx-cos^2x

= 1-cos^2x

= sin^2x

= right hand side