# Thread: trigonometric identity proving need help

1. ## trigonometric identity proving need help

how should i start this

1 - cos^2 theta/ 1 + sin theta = (convert to) sin theta

2. Originally Posted by xahjika
how should i start this

1 - cos^2 theta/ 1 + sin theta = (convert to) sin theta

$1-\frac{\cos^2{\theta}}{1+\sin{\theta}}$

Recall that $\cos^2{\theta} = 1-\sin^2{\theta} = (1-\sin{\theta})(1+\sin{\theta})$

3. it says that

prove that it is an identity

1 - cos^2 theta/ 1 + sin theta = sin theta

4. Originally Posted by xahjika
it says that

prove that it is an identity

1 - cos^2 theta/ 1 + sin theta = sin theta
I have figured it out, and made the edits. But please, in the future, be more clear and add parentheses.

5. That identity is not true. Are you sure you're written it correctly?

Edit: Ah right, I was reading it incorrectly also... nevermind.

6. so sorry i don't know that... i'm just copying what's on the board

7. Originally Posted by Chop Suey
$1-\frac{\cos^2{\theta}}{1+\sin{\theta}}$

Recall that $\cos^2{\theta} = 1-\sin^2{\theta} = (1-\sin{\theta})(1+\sin{\theta})$

with that do i have to foil method this? --> (1 - sin theta)(1 + sin theta)/
1 + sin theta
or cancel the(1 + sin theta).. / 1 + sin theta here --> (1 - sin theta)(1 + sin theta)/ 1 + sin theta

8. is this right?

red means canceled out

1 - sin^2 theta =

(1 - sin theta) (1 + sin theta)/ (1 + sin theta)=

1 - ( 1 - sin theta) = sin theta

9. Originally Posted by xahjika
is this right?

red means canceled out

1 - sin^2 theta =

(1 - sin theta) (1 + sin theta)/ (1 + sin theta)=

1 - ( 1 - sin theta) = sin theta
Yes, you have to cancel out like you just did. There are inconsistencies in your work that you may have to fix.