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प्रश्न
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
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उत्तर
LHS = `sqrt(((1 + cos A)(1 + cos A))/((1 - cos A)(1 + cos A)))`
= `sqrt((1 + cos A)^2/(1 - cos^2 A))`
= `sqrt((1 + cos^2 A + 2cos A)/sin^2 A`
= `(1 + cos A)/sin A`
RHS = `(tan A + sin A)/(tan A sin A)`
= `(sin A(1/cos A + 1))/((sin A/cos A xx sin A)`
= `(sin A( 1 + cos A))/cos A xx cos A/(sin A sin A)`
= `(1 + cos A)/sin A`
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identity:
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
Prove the following trigonometric identities.
(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)
Prove that
`sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ`
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
Prove the following identity :
`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`
