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प्रश्न
Prove the following identities:
`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
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उत्तर
L.H.S. = `sqrt((1 - sinA)/(1 + sinA))`
= `sqrt((1 - sinA)/(1 + sinA) xx (1 + sinA)/(1 + sinA))`
= `sqrt((1 - sin^2A)/(1 + sinA)^2)`
= `sqrt(cos^2A/(1 + sinA)^2)`
= `cosA/(1 + sinA)` = R.H.S.
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संबंधित प्रश्न
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If `tan θ = 13/12`, then cot θ = ?
`5/(sin^2θ) - 5cot^2θ`, complete the activity given below.
Activity:
`5/(sin^2θ) - 5cot^2θ`
= `square (1/(sin^2θ) - cot^2θ)`
= `5(square - cot^2θ) ...[1/(sin^2θ) = square]`
= 5(1)
= `square`
Show that, cotθ + tanθ = cosecθ × secθ
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
(1 + sin A)(1 – sin A) is equal to ______.
