Question

If you know trig please help! Will give brainliest!

Answer 1

Answer:

sin^2α

Step-by-step explanation:

I will just  pose  x instead  of alpha  here to make things simpler

$\tan ^2\left(x\right)\left(2\cos ^2\left(x\right)+\sin ^2\left(x\right)-1\right)$

we know that sin^2x = 1 -  cos^2x so...

$=\left(-1+1-\cos ^2\left(x\right)+2\cos ^2\left(x\right)\right)\tan ^2\left(x\right)$

$=\cos ^2\left(x\right)\tan ^2\left(x\right)$

we can rewrite using trigonometric identities (tan = sin/cos)...

$=\left(\frac{\sin \left(x\right)}{\cos \left(x\right)}\right)^2\cos ^2\left(x\right)\\= \sin ^2\left(x\right)$