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प्रश्न
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
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उत्तर
sinθcotθ + sinθcosecθ = 1 + cosθ
LHS = `sinθcosθ/sinθ + sinθ1/sinθ`
= cosθ + 1 = RHS
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Activity:
L.H.S. = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` ...`[sin^2"A" + square = 1]`
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Activity:
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= `square (1 - (sin^2θ)/(tan^2θ))`
= `tan^2θ (1 - square/((sin^2θ)/(cos^2θ)))`
= `tan^2θ (1 - (sin^2θ)/1 xx (cos^2θ)/square)`
= `tan^2θ (1 - square)`
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= R.H.S.
