SOLUTION: prove the identity (cosθ - sinθ)/(cosθ + sinθ) = sec2θ - tan2θ

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Question 687496: prove the identity (cosθ - sinθ)/(cosθ + sinθ) = sec2θ - tan2θ
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!


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Use the identities  
                    

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The trick here is to replace the 1 by cosē()+sinē(),
so the numerator will become factorable after
rearranging the terms, and we see that the denominator
is factorable as the difference of squares:

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Rearrange the terms and the order of factors in the numerator
to show that it is factorable:

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Factor numerator and denominator:

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Edwin
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