You can put this solution on YOUR website! cot theta - tan theta over cot theta + tan theta = cos 2theta
use x for theta
(cotx-tanx)/(cotx+tanx)=cos2x
start with left side:
(cotx-tanx)/(cotx+tanx)
=[(cosx/sinx)-(sinx/cosx)]/[(cosx/sinx)+(sinx/cosx)]
=[(cos^2x-sin^2x)/(sinxcosx)]/[(cos^2x+sin^2x)/(sinxcosx)]
sinxcosx cancels out, (cos^2x+sin^2x)=1
=(cos^2x-sin^2x)
=cos2x
verified: left side=right side
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