Prove the identity cot2x cos2 x cot2 x cos2 xSolutionLHS

Prove the identity. cot^2x - cos^2 x = cot^2 x cos^2 x

Solution

L.H.S. :

cot²x - cos²x

= cos²x / sin²x - cos²x (as cotx = cosx/sinx)

= (cos²x - cos²x sin²x )/ sin²x

= [cos²x (1 - sin²x)]/sin²x

= (cos²x. cos²x) / sin²x (as 1 - sin²x = cos²x)

= (cos²x / sin²x ) . cos²x

= cot²x . cos²x

= R.H.S.