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Question

Prove L.H.S =R.H.S cosAsinA+1cosA+sinA1= cosecA+cotA

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Solution

cosAsinA+1cosA+sinA1
=cosA(1+sinA)cosA+(1+sinA)
=[cosA(sinA1)]cosA(sinA1)cosA+(sinA1)cosA(sinA1)
=[cosA(sinA1)]2cos2A(sinA1)2
=cos2A+sin2A+12cosA(sinA1)2sinAcos2Asin2A1+2sinA
=22cosAsinA+2cosA2sinA12sin2A1+2sinA [cos2A+sin2A=1]
=1cosAsinA+cosAsinAsinA(1sinA)
=(1+cosA)sinA(1+cosA)sinA(1sinA)
=(1sinA)(1+cosA)sinA(1sinA)
=1+cosAsinA=cscA+cotA


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