Prove that : (cotx - tanx)/(cotx + tanx) = cosx^2 - sinx^2

Expert Answers

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The identity `(cotx - tanx)/(cotx + tanx) = cos^2x - sin^2x` has to be proved.

Start with the left hand side

`(cotx - tanx)/(cotx + tanx)`

=> `((cosx/sinx) - (sinx/cosx))/((cosx/sinx)+(sinx/cosx))`

=> `((cos^2x - sin^2x)/(sinx*cosx))/((cos^2x + sin^2x)/(sinx*cosx))`

=> `(cos^2x - sin^2x)/1`

=> `cos^2x - sin^2x`

which is the right hand side

This proves that `(cotx - tanx)/(cotx + tanx) = cos^2x - sin^2x`

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