Question 28554
This trig indentiy is pretty complex to be thought of derivaties. SO in this indentiy solve by subsitution and develop your own identiy. FIrst we will find what sin^2x equals.


cos^2x-sin^2x=1-2(sin^2x)
cos^2x-sin^2x-1=-2(sin^2x)
-(cos^2x-sin^2x-1)/2=sin^2x
So a new trig identiy is formed. SUbsitute it into the original.


cos^2x-sin^2x = 1-2((-(cos^2x-sin^2x-1)/2) simplify
cos^2x-sin^2x = 1+cos^2x-sin^2x-1
cos^2x-sin^2x = cos^2x-sin^2x


Proven.
Paul.