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प्रश्न
Prove the following identity :
`(1 + tan^2θ)sinθcosθ = tanθ`
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उत्तर
LHS = `(1 + tan^2θ)sinθcosθ`
= `(1 + sin^2θ/cos^2θ)sinθcosθ`
= `((cos^2θ + sin^2θ)/cos^2θ)sinθcosθ`
= `1/cos^2θ xx sinθcosθ` (∵ `cos^2θ + sin2θ = 1`)
= `sinθ/cosθ = tanθ`
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संबंधित प्रश्न
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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
