Asked by krishan
prove that 2sinxcosx-cosx/1 -sinx+sin^2x-cos^2x=cotx
Answers
Answered by
Adithya
LHS = (2sinxcosx-cosx)/(1-sinx-cos^2x+sin^2x)
= (2sinxcosx-cosx)/(sin^2x+cos^2x-sinx-cos^2x+sin^2x)
= (2sinxcosx-cosx)/(2sin^2x+cos^2x)
= cosx(2sinx-1)/sinx(2sinx-1)
= cosx/sinx
= cotx
=RHS
= (2sinxcosx-cosx)/(sin^2x+cos^2x-sinx-cos^2x+sin^2x)
= (2sinxcosx-cosx)/(2sin^2x+cos^2x)
= cosx(2sinx-1)/sinx(2sinx-1)
= cosx/sinx
= cotx
=RHS
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