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# C2 Trig Identities Help! Watch

1. Hey guys I need proving the following identity, where t = theta. :

1-2sin^2 t / cos t + sin t = cos t - sin t.
How can start to use identities on the left hand side?

Many thanks
2. You have on the denominator of the fraction, and no other fractions. This implies that you want to somehow write the on the top of the fraction in terms of (or )... what identities do you know that link these things together?

EDIT: I'm not convinced that the identity you've given is actually valid. Are you sure you've copied it correctly?
3. start from the RHS and go to the LHS. Do the RHS x (cost + sint) / (cost + sint) and go from there
4. (Original post by nuodai)
You have on the denominator of the fraction, and no other fractions. This implies that you want to somehow write the on the top of the fraction in terms of (or )... what identities do you know that link these things together?

EDIT: I'm not convinced that the identity you've given is actually valid. Are you sure you've copied it correctly?
Yes that's right, and I know that sin^2 t = 1 - cos^2 t, so then my fraction would be: 1 - 2(1-cos^2 t) / cos t + sin t?

And yes I believe I have copied it correctly, just to state again it says:

1 - 2sin^2 t / cos t + sin t = cos t - sin t (note the divide sign represents that like a fraction)
Yes that's right, and I know that sin^2 t = 1 - cos^2 t, so then my fraction would be: 1 - 2(1-cos^2 t) / cos t + sin t?

And yes I believe I have copied it correctly, just to state again it says:

1 - 2sin^2 t / cos t + sin t = cos t - sin t (note the divide sign represents that like a fraction)
I just realised your fraction is supposed to be and not like I thought... it's a better idea to use brackets to make it more clear.

Your best bet is to write as . How else can you write ? Then factorise the numerator of the fraction and cancel common factors. [Hint: difference of two squares.]
6. (Original post by nuodai)
I just realised your fraction is supposed to be and not like I thought... it's a better idea to use brackets to make it more clear.

Your best bet is to write as . How else can you write ? Then factorise the numerator of the fraction and cancel common factors. [Hint: difference of two squares.]
Thanks a lot! Repped

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Updated: December 17, 2010
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