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प्रश्न
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
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उत्तर
L.H.S. = `sinA/(1 + cosA)`
= `sinA/(1 + cosA) xx (1 - cosA)/(1 - cosA)`
= `(sinA(1 - cosA))/(1 - cos^2A)`
= `(sinA(1 - cosA))/sin^2A`
= `(1 - cosA)/sinA`
= `1/sinA - cosA/sinA`
= cosec A – cot A = R.H.S.
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संबंधित प्रश्न
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`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ`
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S. = `square`
= `square/(sinθ) + (sinθ)/(cosθ)`
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= `1/(sinθ.cosθ)` ...`[cos^2θ + sin^2θ = square]`
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= `square`
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