Question

prove that cosA/1-tanA+sinA/1-cotA=sinA+cosA​

Answer 1

Step-by-step explanation:

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LHS .

cosa / 1-tana + sina / 1-cot a

(tana = sina/ cosa, cot a = cosa/sina)

cosa/1-(sina/cosa) + sina /1- (cosa/sina)

Taking LCM

cosa/ (cosa - sina)/cosa + {sina / (sina - cosa)/ sina}

cos^2a/ cosa-sina + sin^2a / sina - cosa

Taking - ve common.

cos^2a / cosa - sina - sin^2a / cosa - sina

Taking LCM.

cos^2a - sin^2a/ cosa - sina

{ a^2- b^2 =( a+b)( a-b)}

Applying the identity.

(cosa+ sina )(cosa - sina)/ cosa-sina

cosa + sina = LHS

LHS = RHS .

HENCE PROVED.

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