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प्रश्न
Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.
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उत्तर
LHS = `sqrt((1 + sin θ)/(1 - sin θ) xx (1 + sin θ)/(1 + sin θ))`
= `sqrt((1 + sin θ)^2/(1 - sin^2θ))`
= `sqrt((1 + sin θ)^2/(cos^2θ)`
= `(1 + sin θ)/cos θ = 1/cos θ + sin θ/cos θ`
= sec θ + tan θ
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following identities:
`(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ`
`(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2`
`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`
Prove the following trigonometric identities.
`cos theta/(1 + sin theta) = (1 - sin theta)/cos theta`
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(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
`(sectheta- tan theta)/(sec theta + tan theta) = ( cos ^2 theta)/( (1+ sin theta)^2)`
Prove that:
`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
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