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

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(1807) (Show Source): You can put this solution on YOUR website!


The trick is that if you see any of these:

, , , , you can change them to either  or ,
which are identities for  or  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:

 = 

               = 

               = 

               = 

               = 
Edwin

RELATED QUESTIONS
How do you prove that sin^2 theta equals (sec^2 theta)(cos^2 theta) minus 1/sec^2theta is (answered by MathLover1)

NEED URGENT HELP ON THIS QUESTION! (sin theta/1 + sin theta)- (sin theta/1 - sin theta)... (answered by lwsshak3)

how do i prove 1+sin theta ____________ = tan power of 2 (pie/2 + theta/2) 1- sin... (answered by Alan3354)

How do I express cos(theta) in terms of sin(theta)? I'm taking an online pre-cal... (answered by josgarithmetic)

Hi. Please help me verify this equation as an identity: {{{sec(theta)/tan(theta)}}} +... (answered by Alan3354,AnlytcPhil)

How do you find csc theta in terms of cos theta if theta is in quadrant four ? I have... (answered by Alan3354)

prove {{{sin^2(theta)=(1/2)(1-cos2(theta))}}} is an... (answered by Leaf W.)

Verify that sec theta/sin theta * cot theta/csc theta = csc theta is an identity, help? (answered by richard1234)

How do i establish the identity sin^3 theta - cos^3 theta/sin theta - cos theta = 1 +... (answered by dkppathak)