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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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Activity:
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= `square (1/(sin^2θ) - cot^2θ)`
= `5(square - cot^2θ) ...[1/(sin^2θ) = square]`
= 5(1)
= `square`
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