Question

Hey! Is there a trig identity for sin^2 theta divided by cos^2 theta? Thanks :)

Answer 1

Do you have a particular use for one?

Answer 2

I need to prove an identity and that's part of it. I wanted to see if you could switch it to something else.

Answer 3

The one I was first thinking of was:
\( \displaystyle \frac{\sin ^2 \theta}{\cos ^2 \theta} = \left( \frac{\sin \theta}{\cos \theta} \right) ^2 \)
But a more useful one may depend on the context. :)

Answer 4

** That one is going towards tan^2 theta

Answer 5

ok thanks! I'll try that :)

Answer 6

After that one, you probably have a few options transforming it via \(\sin ^2 \theta + \cos ^2 \theta = 1\), but again if you are having troubles you can just post up the original problem and we can work on it that way. :)

Answer 7

great thanks! Im going to have a little play around with it and see if I can work it out. If Im having trouble I'll post it up. Thanks so much :)

Answer 8

You're welcome! Best of luck! :)

Answer 9

\[(\sin^{2} Θ+4\sinΘ+3)/(\cos ^{2}Θ)=(3+\sinΘ)/(1-\sin \Theta)\]
- I've already tried to change the (cos^2 Θ) to (1-sin^2 Θ) but im not to sure where to go from there
- I've tried to change the LHS to (tan^2Θ) + (4sinΘ+3)/(cos ^2Θ) but I still get stuck

Answer 10

Have you tried factoring the LHS's numerator?

Answer 11

ok so it would be (sin theta + 1) (sin theta +3)?

Answer 12

Yes, that is correct.

Answer 13

and then can you do difference of two squares to the denominator, once its changed to (1-sin^2 theta)?

Answer 14

Yep. You have: 1^2 - (sin theta)^2, a difference of squares may also be factored. :)

Answer 15

so... (1 - sin theta) (1+ sin theta) then you cancel the (sin theta +1) from the numerator and denominator and are left with (sin theta + 3)/(1 - sin theta)!!! YAY!!

Answer 16

There you go! Great! :D

Answer 17

Thank You! Just needed that little hint about factorising the numerator :)

Answer 18

Yep. Sometimes it is the Algebra that comes back to haunt us!
Reminds me of the Calculus problem of an integral of e^x cos x, you end up solving it by using basic Algebra after using all the Calculus ideas beforehand, the least likely solution. :P

Answer 19

haha! yep :) Thank You!!