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