### Home > INT3 > Chapter 12 > Lesson 12.2.1 > Problem 12-85

12-85.

Rewrite each of the following expressions in a simpler form. Homework Help ✎

cos

^{2}(*θ*– π) + sin^{2}(*θ*– π)cos

^{2}(2*w*) – sin^{2}(2*w*)

Review your work from problem 12-73 or the formulas in the Math Notes box in Lesson 12.2.3.

Remember:

cos²(*θ*) + sin²(*θ*) = 1.

The variable here is different, but will this change the identity? If you aren't sure, let *U = θ − π*

1

Remember:

cos²(*x*) − sin²(x) = cos(2*x*).

Try writing sin(*θ*) as opposite over hypotenuse and cos(*θ*) as adjacent over hypotenuse.

Simplify the complex fraction. Is the new ratio equivalent to another trig ratio?

tan(*θ*)