Question

PLEASE HELP! Prove: tan2 θ•cos2 θ + cos2 θ = 1. You must show all work

Answer 1

hint:

\(\tan^2(\theta)\cos^2(\theta)=\frac{\sin^2(\theta)}{\cos^2(\theta)}\cos^2(\theta)=\frac{\sin^2(\theta)}{\cancel{\cos^2(\theta)}}\cancel{\cos^2(\theta)}\)

Answer 2

Is sin^2 T = 1??

Answer 3

another hint:

There was a dude named Pythagoras, and he and his friends did some pretty cool stuff.

Answer 4

Haha I understand, what do I put into the pythagorean thereom?

Answer 5

correct

Answer 6

So sin^2 T = 1 is the final portion of this answer?

Answer 7

\(\tan^2(\theta)\cos^2(\theta)+\cos^2(\theta)=\frac{\sin^2(\theta)}{\cos^2(\theta)}\cos^2(\theta)+\cos^2(\theta)=\\\frac{\sin^2(\theta)}{\cancel{\cos^2(\theta)}}\cancel{\cos^2(\theta)}+\cos^2(\theta)=\sin^2(\theta)+\cos^2(\theta)= \ \huge ?\)

Answer 8

1?

Answer 9

@zzr0ck3r

Answer 10

correct, that is the Pythagorean theorem \(\cos^2(x)+\sin^2(x) = 1\) for all \(x\).

Answer 11

Thank you so much @zzr0ck3r

Answer 12

np.