Home > CCA2 > Chapter 12 > Lesson 12.2.1 > Problem12-90

12-90.

Rewrite each of the following expressions in a simpler form.

1. $\cos^2(θ−\pi)+\sin^2\left(\theta-\pi\right)$

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 $U = θ - π$

$1$

1. $\cos^2\left(2w\right)-\sin^2\left(2w\right)$

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

1. $\frac { \operatorname { sin } \theta } { \operatorname { cos } \theta }$

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?

$\tan(θ)$