show that cosA /1-sinA + sinA/1-cosA +1 = sinA.cosA/(1-sinA)(1-cosA)
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Answer:
CosA/1-sinA + sinA/1-cosA +1=sinAcosA/(1-sinA)(1-cosA)
Solve LHS
=cosA(1-cosA) + sinA(1-sinA) + (1-sinA)(1-cosA//(1-sinA)(1-cosA)
=cosA-cos^2A + sinA-sin^2A+1-cosA-sinA+sinAcosA//(1-sinA)(1-cosA)
=cosA-cosA+sinA-sinA-(sin^2A+cos^2A)+1+sinAcosA/(1-sinA)(1-cosA)
=0+0-(1)+1+sinAcosA/(1-sinA)(1-cosA)
=sinAcosA/(1-sinA)(1-cosA)
Hence, LHS=RHS
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