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प्रश्न
Prove the following identities:
`((1 + tan^2A)cotA)/(cosec^2A) = tan A`
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उत्तर
L.H.S. = `((1 + tan^2A)cotA)/(cosec^2A)`
= `(sec^2A cotA)/(cosec^2A` ...(∵ sec2 A = 1 + tan2 A)
= `(1/(cos^2A) xx (cosA)/(sinA))/(1/(sin^2A))`
= `(1/(cosA sinA))/(1/(sin^2A))`
= `sinA/cosA`
= tan A = R.H.S.
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Activity:
L.H.S. = `square`
= `square/(sinθ) + (sinθ)/(cosθ)`
= `(cos^2θ + sin^2θ)/square`
= `1/(sinθ.cosθ)` ...`[cos^2θ + sin^2θ = square]`
= `1/(sinθ) xx 1/square`
= `square`
= R.H.S.
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