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प्रश्न
\[\frac{x^2 - 1}{2x}\] is equal to
विकल्प
sec θ + tan θ
sec θ − tan θ
sec2 θ + tan2 θ
sec2 θ − tan2 θ
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उत्तर
The given expression is `sqrt ((1+sinθ)/(1-sinθ))`
Multiplying both the numerator and denominator under the root by `1+ sinθ`, we have
`sqrt (((1+ sinθ)(1+sin θ))/((1+sin θ)(1-sinθ)))`
`=sqrt((1+sinθ)/((1- sin^2θ)))`
`= sqrt((1+ sinθ)^2/cos^2θ)`
=`(1+sinθ)/cosθ`
=` 1/cosθ+sinθ/cosθ`
=` sec θ+tan θ`
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संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Prove the following trigonometric identities.
`(1 + cos A)/sin^2 A = 1/(1 - cos A)`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
Prove the following trigonometric identities.
if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
Prove the following identities:
`1/(1 + cosA) + 1/(1 - cosA) = 2cosec^2A`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
If`( 2 sin theta + 3 cos theta) =2 , " prove that " (3 sin theta - 2 cos theta) = +- 3.`
If m = ` ( cos theta - sin theta ) and n = ( cos theta + sin theta ) "then show that" sqrt(m/n) + sqrt(n/m) = 2/sqrt(1-tan^2 theta)`.
\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to
Prove the following identity :
`(1 - tanA)^2 + (1 + tanA)^2 = 2sec^2A`
Prove the following identity :
`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
tan θ cosec2 θ – tan θ is equal to
Prove that `cot^2 "A" [(sec "A" - 1)/(1 + sin "A")] + sec^2 "A" [(sin"A" - 1)/(1 + sec"A")]` = 0
`5/(sin^2theta) - 5cot^2theta`, complete the activity given below.
Activity:
`5/(sin^2theta) - 5cot^2theta`
= `square (1/(sin^2theta) - cot^2theta)`
= `5(square - cot^2theta) ......[1/(sin^2theta) = square]`
= 5(1)
= `square`
`sqrt((1 - cos^2theta) sec^2 theta) = tan theta`
Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`
