Question 365339
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.