(1+cotA+tanA)(sinA - cosA)
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Sia ? 6 years, 1 month ago
L.H.S
= (1 + cotA + tanA) (sinA - cosA)
= sinA - cosA + cotA sinA - cotA cosA + sinA tanA - tanA cosA
=sinA−cosA+cosAsinA×sinA−cotAcosA+sinAtanA−sinAcosA×cosA
= sinA - cosA + cosA - cotA cosA + sinA tanA - sinA
= sinA tanA - cotA cosA........(1)
Now taking ;
secAcosec2A−cosecAsec2A
=1cosA1sin2A−1sinA1cos2A
=sin2AcosA−cos2AsinA
=sinA×sinAcosA−cosA×cosAsinA
=sinA×tanA−cosA×cotA.......(2)
From (1) & (2),
(1 + cotA + tanA) (sinA - cosA) = secAcosec2A−cosecAsec2A = sinA.tanA - cosA.cotA
Hence, Proved.
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