# 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

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Trigonometry Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Trigonometry-basics 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)   (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)   (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