cos a+sin a/cos a-sin a -cos a- sin a/cos a+ sin a= 2tan 2a
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LHS
(cosa + sina)/(cosa - sina) - (cosa - sina)/(cosa + sina)
= ((cosa + sina)^2 - (cosa - sina)^2) / (cosa + sina)(cosa - sina)
= (cosa + sina + cosa - sina)(cosa + sina - cosa + sina) / (cos^2a - sin^2a)
= 2cosa*2sina/(cos^2a - sin^2a)
(2*sina*cosa = sin2a and cos^2a - sin^2a = cos2a)
= 2sin2a/cos2a = 2*tan2a = RHS Ans...
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explanation in the snap attached to this answer.
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