Question:
cos2a/1-sin2a=tan(45°+ a)
Answer:
Given
cos2a/1-sin2a
= (cos2 a - sin2 a)/(sin2 a +cos2 a - 2*sina*cosa) (since cos2a =cos2 a - sin2 a and sin2 a +cos2 a = 1)
= (cosa - sina)*(cosa + sina)/(cosa - sina)2
= (cosa + sina)/(cosa - sina)
={cosa*(1+ sina/cosa)}/{cosa*(1- sina/cosa)}
= (1+ tan a)*(1 - tan a)
= (1+ tan a)*(1 - 1*tan a)
= (tan45° + tan a)*(1- tan 45° *tan a) (since tan 45° = 1)
= tan(45° + a)
So cos2a/(1-sin2a) = tan(45° + a)
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