Kindly Prove That

CosA / 1 - TanA + SinA / 1 - CotA = CosA + SinA
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1 Answer

cosA/(1-tanA)=cos2A/(cosA-sinA) (multiply top and bottom by cosA);

sinA/(1-cotA)=sin2A/(sinA-cosA) (multiply top and bottom by sinA).

sinA-cosA=-(cosA-sinA) so we have:

cos2A/(cosA-sinA)-sin2A/(cosA-sinA)=

(cos2A-sin2A)/(cosA-sinA)=

(cosA-sinA)(cosA+sinA)/(cosA-sinA)=cosA+sinA QED.

by Top Rated User (1.2m points)

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