Question

Complete the proof of the identity by choosing the rule that justifies each step.(1-cosx)(1+cosx)=sin^2x

Answer 1

You have the following expression:

$(1+cosx)(1-\cos x)=\sin ^2x$

To verify the identity, you have that the left side of the equation becomes:

(1 + cosx)(1 - cosx) = (1 - cos^2 x)

because of the product of an expression by its conjugate result in a difference of squares. Or simplfy by expanding the factors and simplying.

Next, you have:

1 - cos^2 x = sin^2 x

because the Pythagorean identity.

Then, the identity is verified.