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प्रश्न
Prove that `( sintheta - 2 sin ^3 theta ) = ( 2 cos ^3 theta - cos theta) tan theta`
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उत्तर
RHS = `(2 cos^3 theta - cos theta) tan theta`
=`(2 cos^2 theta - 1) cos theta xx sin theta/ cos theta`
=`[2(1- sin^2 theta ) -1] sin theta`
=` (2-2 sin^2 theta -1 ) sin theta`
=` (1-2 sin^2 theta ) sin theta`
=`( sin theta -2 sin^3 theta )`
=LHS
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Activity:
L.H.S. = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` ...`[sin^2"A" + square = 1]`
= `square` – cos2A ...[sin2A = 1 – cos2A]
= `square`
= R.H.S.
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1 + `square` = cosec2θ
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`square/square` = cosec2θ ......[Taking root on the both side]
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and sin θ = `1/("cosec" θ)`
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∴ sin θ = `9/41`
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