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प्रश्न
Prove the following identity :
`sec^2A + cosec^2A = sec^2Acosec^2A`
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उत्तर
LHS = `sec^2A + cosec^2A`
= `1/cos^2A + 1/sin^2A = (sin^2A + cos^2A)/(cos^2A.sin^2A)`
= `1/(cos^2A.sin^2A) = sec^2Acosec^2A` = RHS
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Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
