SOLUTION: Hi. How do I prove that this is an identity?? I really don't get how this works... (1-3cosTheta - 4cos^2 Theta)/ sin^2 Theta = (1-4cosTheta)/1-cosTheta

Algebra ->  Trigonometry-basics -> SOLUTION: Hi. How do I prove that this is an identity?? I really don't get how this works... (1-3cosTheta - 4cos^2 Theta)/ sin^2 Theta = (1-4cosTheta)/1-cosTheta       Log On


   

Question 602435: Hi. How do I prove that this is an identity?? I really don't get how this works...

(1-3cosTheta - 4cos^2 Theta)/ sin^2 Theta = (1-4cosTheta)/1-cosTheta

Oh, and if you can, please explain how you arrived at the answer as well. I really don't get how our teacher explains this, you see. Thanks a bunch to those who answer!
Answer by AnlytcPhil(1810) About Me  (Show Source):
You can put this solution on YOUR website!

The trick is that if you see any of these:

1+%2B+cos%28theta%29, 1+-+cos%28theta%29, 1+%2B+sin%28theta%29, 1+-+sin%28theta%29, you can change them to either 1+-+cos%5E2%28theta%29 or 1+-+sin%5E2%28theta%29,
which are identities for sin%5E2%28theta%29 or cos%5E2%28theta%29 respectively, by multiplying and
dividing by the conjugate.  There is one of these on the bottom of the right
side, so start with the right side and do just that:

%281-3cos%28theta%29-4cos%5E2%28theta%29%29%2Fsin%5E2%28theta%29%29 = %281-4cos%28theta%29%29%2F%281-cos%28theta%29%29

               = 

               = 

               = %281-3cos%28theta%29-4cos%5E2%28theta%29%29%2F%281-cos%5E2%28theta%29%29

               = %281-3cos%28theta%29-4cos%5E2%28theta%29%29%2Fsin%5E2%28theta%29
Edwin