Question

Verify the identity secx-secx sin^2x=cosx

Answer 1

hello :
* secx = 1/cosx
cos²x+sin²x= 1
**sin²x = 1-cos²x
by (*) :
secx-secx sin²x=(1/cosx) -(1/cosx) sin²x
= (1/cosx)(1- sin²x)....factory :(1/cosx)
by(**)
secx-secx sin²x = (1/cosx)cos²x
secx-secx sin²x = cosx ...( simplify by : cosx)