Question

Prove: tan^2 θ cos^2 θ + cos^2 θ = 1. You must show all work.

Answer 1

Hint:

Factor out \(\cos^2\theta\)

Answer 2

How do I do that?

Answer 3

After factoring out \(\cos^2\theta\) you should have

\(\cos^2 \theta (\tan^2 \theta + 1) = 1\)

Answer 4

Next divide both sides by \(\cos^2\theta\)

Answer 5

tan^2x=sin^2x/cos^2x

cosines cancel and you get an identity.

Answer 6

Or you can do that which would be better. @SolomonZelman just couldn't help himself.

Answer 7

I don't really understand the last sentence of your comment :) -:(

Answer 8

@SolomonZelman Can you help with one more

Answer 9

When I "help" myself, posting the solution and answer, I get suspended. So why would I do that ?

Answer 10

Gamer, Perhaps I can:) I'll try to flex my weak brains.

Answer 11

I did a problem like that before with you but I seem to have forgot it @SolomonZelman

Answer 12

attach not working -:(

Answer 13

Actually, it would have been better to divide both sides by \(\cos^2 \theta\) because then you would have seen that

\(\tan^2\theta + 1 = \sec^2 \theta\)

Answer 14

@Hero Can you please help"?

Answer 15

At that point you could have done this:

\(\cos^2\theta(\sec^2\theta) = 1\)

Answer 16

And since you know that \(\sec^2\theta = \dfrac{1}{\cos^2\theta}\)

You could have written it this way for the next step:

\(\cos^2\theta\left(\dfrac{1}{\cos^2\theta}\right) = 1\)

Answer 17

@Hero Help with my other question

Answer 18

Can you??

Answer 19

Yes, but post it as a new question

Answer 20

Sure but don't leave

Answer 21

@Hero http://openstudy.com/study#/updates/538d3047e4b0d2ed7ed7c51e

Answer 22

Try your best to post only one question at a time. Don't post two questions in the same discussion unless they are purposefully related to each other. Like for example Part A, and Part B, of Question 1