CPM Homework Help : INT3 Problem 12-85

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12-85.

Rewrite each of the following expressions in a simpler form.

$\cos^2(θ−\pi)+\sin^2\left(\theta-\pi\right)$
Hint (a):
Remember:
$\cos^2\left(\theta\right)+\sin^2\left(\theta\right)=1$ .
The variable here is different, but will this change the identity? If you aren't sure, let $U = θ - π$
Answer (a):
$1$

$\cos^2\left(2w\right)-\sin^2\left(2w\right)$
Hint (b):
Remember:
$\cos^2\left(x\right)-\sin^2\left(x\right)=\cos\left(2x\right)$ .

$\frac { \operatorname { sin } \theta } { \operatorname { cos } \theta }$
Hint (c):
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?
Answer (c):
$\tan(θ)$

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