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प्रश्न
Prove the following identities:
`1/(tan A + cot A) = cos A sin A`
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उत्तर
L.H.S. = `1/(tan A + cot A)`
= `1/((sin A)/(cos A) + (cos A)/(sin A))`
= `1/((sin^2A + cos^2A)/(sin A cos A))`
= `1/(1/(sin A cos A))` ...(∵ sin2A + cos2A = 1)
= sin A cos A
= R.H.S.
संबंधित प्रश्न
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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)`
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∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
