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Question

Prove that :
cosA1sinA+sinA1cosA+1=sinAcosA(1sinA)(1cosA)

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Solution

we have
LHS=cosA1sinA+sinA1cosA+1

LHS=cosA(1cosA)+sinA(1cosA)+(1sinA)(1+cosA)sinA(1cosA)+(1sinA)(1+cosA)

LHS=cosAcos2A+sinAsin2A+1sinAcosA+sinAcosAsinA(1cosA)+(1sinA)(1+cosA)

LHS=(cosA+sinA)(cos2Asin2A)+1(cosA+,sinA)+sinAcosAsinA(1cosA)+(1sinA)(1+cosA)

LHS=(cosA+sinA)1+1(cosA+sinA)+sinA+cosAsinA(1cosA)+(1sinA)(1+cosA)

LHS=sinAcosAsinA(1cosA)+(1sinA)(1+cosA) =RHS

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