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QUESTION
How do you verify ##(1-tan^2x) / (1+tan^2x) = 1-2sin^2##?
##L.H.S=R.H.S##
##L.H.S = (1-tan^2x)/(1+tan^2x)## ##=(1-sin^2x/cos^2x)/(1+sin^2x/cos^2x## ##=((cos^2x-sin^2x)/cos^2x)/((cos^2x+sin^2x)/cos^2x)## ##=(cos^2x-sin^2x)/(cos^2x+sin^2x)## ##=(cos^2x-sin^2x)/1 ; Since cos^2x+sin^2x=1;cos^2x=1-sin^2x## ##=cos^2x-sin^2x## ##=1-sin^2x-sin^2x## ##=1-2sin^2x## ##=R.H.S##
