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प्रश्न
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
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उत्तर
LHS = `(1 + cot^2 θ/(1 + cosec θ))`
= `(1 + cosec θ + cosec^2 θ - 1)/(1 + cosec θ)`
= `(cosec θ(1 + cosec θ))/(1 + cosec θ)`
= cosec θ
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities.
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cosec4 A (1 – cos4 A) – 2 cot2 A = 1
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Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
