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(1+cotA+tanA)(sinA - cosA)

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(1+cotA+tanA)(sinA - cosA)
  • 1 answers

Sia ? 6 years, 1 month ago

L.H.S 
= (1 + cotA + tanA) (sinA - cosA)
= sinA - cosA + cotA sinA - cotA cosA + sinA tanA - tanA cosA
=sinAcosA+cosAsinA×sinAcotAcosA+sinAtanAsinAcosA×cosA
= sinA - cosA + cosA - cotA cosA + sinA tanA - sinA
=  sinA tanA - cotA cosA........(1)
Now taking ;
secAcosec2AcosecAsec2A
=1cosA1sin2A1sinA1cos2A
=sin2AcosAcos2AsinA
=sinA×sinAcosAcosA×cosAsinA
=sinA×tanAcosA×cotA.......(2)
From (1) & (2),
(1 + cotA + tanA) (sinA - cosA) = secAcosec2AcosecAsec2A = sinA.tanA - cosA.cotA 
Hence, Proved.

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