cosA-sinA+1/cosA+sinA-1=cosecA+cotA
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Answer:
RHS,
=cosecA+cotA
=1/sinA+cosA/sinA
=1+cosA/sinA
LHS,
dividing and multiplying by sinA
=sinA(cosA-sinA+1)/sinA(cosA+sinA-1)
=sinAcosA-sin²A+sinA/sinA(cosA+sinA-1)
=sinAcosA+sinA-(1-cos²A)/sinA(cosA+sinA-1)
=sinA(cosA+1)-(1-cosA)(1+cosA)/sinA(cosA+sinA-1)
=(1+cosA)(sinA-cosA+1)/sinA(cosA+sinA-1)
=1+cosA/sinA
∴LHS=RHS
PROVED!!
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