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प्रश्न
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
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उत्तर
`sqrt((1 - cosA)/(1 + cosA))`
= `sqrt((1 - cosA)/(1 + cosA) xx (1 + cosA)/(1 + cosA))`
= `sqrt((1 - cos^2A)/(1 + cosA)^2)`
= `sqrt(sin^2A/(1 + cosA)^2)`
= `sinA/(1 + cosA)`
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संबंधित प्रश्न
Prove the following trigonometric identities
`cos theta/(1 - sin theta) = (1 + sin theta)/cos theta`
Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
`cos^2 theta + 1/((1+ cot^2 theta )) =1`
`(sin theta +cos theta )/(sin theta - cos theta)+(sin theta- cos theta)/(sin theta + cos theta) = 2/((sin^2 theta - cos ^2 theta)) = 2/((2 sin^2 theta -1))`
What is the value of (1 + cot2 θ) sin2 θ?
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A.
Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
If `tan θ = 9/40`, complete the activity to find the value of sec θ.
Activity:
sec2θ = 1 + `square` ...[Fundamental trigonometric identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square`
sec θ = `square`
