Question

Verify the identity
cotx-tanx all over cot^2x- tan^2x= sinxcosx

Answer 1

How would you go to factor ( cot^2x- tan^2x)? Factoring this will make your life much easier.

Answer 2

(cotx-tanx)/(cot^2x- tan^2x)
=(cotx-tanx)/ ( (cotx-tanx) * (cotx+tanx) )
=1/(cotx+tanx)

Answer 3

1/( (cosx/sinx) + (sinx/cosx) )
=1/ ( (cos^2x+ sin^2x) / (cosx*sinx) ) = cosx*sinx/(cos^2x+ sin^2x)
= cosxsinx as we know (cos^2x+ sin^2x)=1