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प्रश्न
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
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उत्तर
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
= `(1 + cosA)/(1 - cosA).(1 + cosA)/(1 + cosA)`
= `((1 + cosA)^2)/(1 - cos^2A) = (1 + cosA)^2/sin^2A`
= `[(1 + cosA)/sinA]^2 = [1/sinA + cosA/sinA]^2`
= `(cosecA + cotA)^2`
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संबंधित प्रश्न
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Prove that : `tan"A"/(1 - cot"A") + cot"A"/(1 - tan"A") = sec"A".cosec"A" + 1`.
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Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
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= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
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