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प्रश्न
Prove the following identity :
`(1 + tan^2θ)sinθcosθ = tanθ`
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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= `cos^2theta xx square .....[1 + tan^2theta = square]`
= `(cos theta xx square)^2`
= 12
= 1
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