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Question

Prove that 1+cscA+cotA1+cscAcotA=cscA+cotA1cotAcscA+1

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Solution

LHS:
1+cscA+cotA1+cscAcotA
=sinA+cosA+1sinAcosA+1
=(sinA+cosA+1sinAcosA+1)(sinA+cosA+1sinA+cosA+1)
=2[1+sinA+cosA+sinAcosA]2sin2A+2sinA=1+cosAsinA
RHS:
1+cscA+cotA1cscAcotA
=sinA+cosA+1sinA+cosA1
=(sinA+cosA+1sinA+cosA1)(sinA+cosA+1sinA+cosA+1)
=2[1sinA+cosAsinAcosA]2sin2A+2sinA=1+cosAsinA
LHS=RHS.

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