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प्रश्न
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
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उत्तर
L.H.S. = `(1 - sinA)/(1 + sinA)`
= `(1 - sinA)/(1 + sinA) xx (1 - sinA)/(1 - sinA)`
= `(1 - sinA)^2/(1 - sin^2A`
= `(1 - sinA)^2/cos^2A`
= `((1 - sinA)/cosA)^2`
= `(1/cosA - sinA/cosA)^2`
= `(secA - tanA)^2`
= R.H.S.
संबंधित प्रश्न
Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
Prove the following trigonometric identities.
`(1 + sin θ)/cos θ+ cos θ/(1 + sin θ) = 2 sec θ`
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following identities:
`cot^2A/(cosecA + 1)^2 = (1 - sinA)/(1 + sinA)`
Prove the following identities:
(1 + tan A + sec A) (1 + cot A – cosec A) = 2
Prove that:
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove that cosec θ – cot θ = `sin theta/(1 + cos theta)`
