sinA(1+tanA)+cosA(1+cotA)= secA+cosecA
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Answer:
sinA(1+tanA)+cosA(1+cotA)= secA+cosecA
Step-by-step explanation:
L.H.S = sinA(1+tanA)+cosA(1+cotA)
= sinA( 1 + sinA/cosA) + cosA(1 + cosA/sinA)
= sinA + sin^2A/cosA + cosA + cos^2A/sinA
= (sinA + cos^2A/sinA) + ( sin^2A/cosA + cosA)
= (sin^2A + cos^2A)/sinA + (sin^2A + cos^2A)/cosA
= 1/sinA + 1/cosA
= cosecA + secA = R.H.S
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