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प्रश्न
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
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उत्तर
L.H.S. = `cosecA + cotA`
= `(cosecA + cotA)/1 xx (cosecA - cotA)/(cosecA - cotA)`
= `(cosec^2A - cot^2A)/(cosecA - cotA)`
= `(1 + cot^2A - cot^2A)/(cosecA - cotA)`
= `1/(cosecA - cotA)` = R.H.S.
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 + cos A)/sin^2 A = 1/(1 - cos A)`
Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
Prove the following identities:
`(1 + sin A)/(1 - sin A) = (cosec A + 1)/(cosec A - 1)`
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = sec A + tan A`
If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p.
`(1+ tan theta + cot theta )(sintheta - cos theta) = ((sec theta)/ (cosec^2 theta)-( cosec theta)/(sec^2 theta))`
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
