prove that (sinA+cos A) (tanA+cotA) =secA+cosecA
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we have to prove that (sinA+cosA)(tanA+cotA)= secA+cosecA
so taking lhs= sinA+cosA ×tanA+cotA
(sinA+cosA)(sinA/cosA+cosA/sinA)
(sinA+cosA)(sin^2A+cos^2A/sinAcosA)
(sinA+cosA)(1/sinAcosA)
(sinA+cosA/sinAcosA)
(1/sinA+1/cosA)
secA+ cosecA
so taking lhs= sinA+cosA ×tanA+cotA
(sinA+cosA)(sinA/cosA+cosA/sinA)
(sinA+cosA)(sin^2A+cos^2A/sinAcosA)
(sinA+cosA)(1/sinAcosA)
(sinA+cosA/sinAcosA)
(1/sinA+1/cosA)
secA+ cosecA
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