Prove that: (secA+cosecA)(sinA+cosA)=tanA+cotA+2=2+secAcosecA
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Answer: L.H.S.=(secA+cosecA) (sin A+cosA)
=secA(sinA+cosA) + cosecA(sinA+cosA)
=sinA*secA +cosA*secA +cosecA*sinA +cosecA*cosA
=sinA/cosA +1+1+cosA/sinA
=2+sinA/cosA+cosA/sinA
=2+sin^2 A+cos^2 A /sinA*cosA
=2+ 1/sinA*cosA (sin^2 A+cos^2 A=1)
=2+secA*cosecA=RHS
Hence Proved.
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