How do you prove $(1 + sin 2A) / (cos 2A) = (cos A + sin A) / (cos A - sin A)$ ?

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Answer 1 · 2015-04-23T20:21:32

$(1+sin(2A))/(cos(2A))$

$= (1+2sin(A)cos(A))/(cos^2(A)-sin^2(A))$

$= (cos^2(A)+sin^2(A) +2sin(A)cos(A))/((cos(A)-sin(A)) * (cos(A)+sin(A)))$

$= (cos(A)+sin(A))^2/((cos(A)-sin(A)) * (cos(A)+sin(A)))$

$= (cos(A)+sin(A))/(cos(A)-sin(A))$

How do you prove (1 + sin 2A) / (cos 2A) = (cos A + sin A) / (cos A - sin A)(1 + sin 2A) / (cos 2A) = (cos A + sin A) / (cos A - sin A)?