# trigonometric identity proving need help

• Dec 17th 2008, 12:48 AM
xahjika
trigonometric identity proving need help
how should i start this

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

• Dec 17th 2008, 12:58 AM
Chop Suey
Quote:

Originally Posted by xahjika
how should i start this

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

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

Recall that $\displaystyle \cos^2{\theta} = 1-\sin^2{\theta} = (1-\sin{\theta})(1+\sin{\theta})$
• Dec 17th 2008, 01:02 AM
xahjika
it says that

prove that it is an identity

1 - cos^2 theta/ 1 + sin theta = sin theta
• Dec 17th 2008, 01:04 AM
Chop Suey
Quote:

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.
• Dec 17th 2008, 01:05 AM
Mush
That identity is not true. Are you sure you're written it correctly?

Edit: Ah right, I was reading it incorrectly also... nevermind.
• Dec 17th 2008, 01:46 AM
xahjika
so sorry i don't know that... i'm just copying what's on the board
• Dec 17th 2008, 02:12 AM
xahjika
Quote:

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

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

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
• Dec 17th 2008, 05:34 AM
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
• Dec 17th 2008, 06:33 AM
Chop Suey
Quote:

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.