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Question

Solve
cos2 A1tan A+sin3Asin Acos A=1+sin A cos A

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Solution

cos2 A1tan A+sin3Asin Acos A=1+sin A cos ALHS: cos2 A1Sin Acos A+sin3Asin Acos A=cos3 Acos Asin Asin3 Acos Asin A=cos3 Asin3Acos Asin A=(cos Asin A)(cos2 A+sin2A)(cos Asin A)
= 1 + sin A cos A = R.H.S proved
(Using identity a3b3=(ab)(a2+ab+b2))

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