Advertisements
Advertisements
प्रश्न
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
Advertisements
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 that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
Prove the following trigonometric identity.
`(sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta - tan theta)`
Prove the following identities:
`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`
Write the value of sin A cos (90° − A) + cos A sin (90° − A).
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Prove that `(tan(90 - θ) + cot(90 - θ))/("cosec" θ) = sec θ`.
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
