SOLUTION: I have a homework problem for trigonometry that is stumping me. it is to verify the identity: cot^2x-cos^2x= cot^2xcos^2x. I have to make both sides of the equation equal. I

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: I have a homework problem for trigonometry that is stumping me. it is to verify the identity: cot^2x-cos^2x= cot^2xcos^2x. I have to make both sides of the equation equal. I      Log On

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Question 365339: I have a homework problem for trigonometry that is stumping me. it is to verify the identity:
cot^2x-cos^2x= cot^2xcos^2x.
I have to make both sides of the equation equal. I have tried using identities such as cot^2x=csc^2x-1, but nothing seems to be working. Thanks for your help!
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(28595) About Me  (Show Source):
You can put this solution on YOUR website!
cot^2x-cos^2x= cot^2xcos^2x .... Start with the given equation.


I'm only going to manipulate the right side.


cot^2x-cos^2x= (csc^2x-1)cos^2x ... Plug in cot^2x=csc^2x-1


cot^2x-cos^2x= csc^2xcos^2x-cos^2x ... Distribute.


cot^2x-cos^2x= ( 1/(sin^2x) )cos^2x-cos^2x ... Use the identity csc(x)=1/sin(x).


cot^2x-cos^2x= (cos^2x)/(sin^2x)-cos^2x ... Multiply


cot^2x-cos^2x= cot^2x-cos^2x ... Use the identity (cos(x))/(sin(x))=cot(x).


So this verifies the identity.

Answer by Alan3354(30993) About Me  (Show Source):
You can put this solution on YOUR website!
cot^2x-cos^2x= cot^2xcos^2x
Change to sines and cosines
(cos^2/sin^2) - cos^2 = (cos^2/sin^2)*cos^2
Divide by cos^2
(1/sin^2) - 1 = cos^2/sin^2
Multiply by sin^2
1 - sin^2 = cos^2