Question 671602
Given
(1) cos^2x = 1 - cos^2x*tan^2x
Use the ID
(2) tanx = sinx/cosx, easily proven.
Then 
(3) tan^2x = sin^2x/cos^2x
Substitute (3) into (1) and get
(4) cos^2x = 1 - sin^2x or
(5) sin^2x + cos^2x = 1 another easily proven ID