Advertisements
Advertisements
प्रश्न
Prove the following identities:
`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
Advertisements
उत्तर
L.H.S. = `(cosecA-1)/(cosecA+1)`
= `(cosecA - 1)/(cosecA + 1) xx (cosecA + 1)/(cosecA + 1)`
= `(cosec^2A - 1)/(cosecA + 1)^2`
= `cot^2A/(cosecA + 1)^2`
= `(cos^2A/sin^2A)/(1/sinA + 1)^2`
= `(cosA/(1 + sinA))^2` = RHS.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 - tan^2 A)/(cot^2 A -1) = tan^2 A`
Prove the following trigonometric identities.
`1 + cot^2 theta/(1 + cosec theta) = cosec theta`
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
If `( tan theta + sin theta ) = m and ( tan theta - sin theta ) = n " prove that "(m^2-n^2)^2 = 16 mn .`
Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`
Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.
Prove the following identity :
`sec^2A + cosec^2A = sec^2Acosec^2A`
Prove the following identity :
`(1 + tan^2θ)sinθcosθ = tanθ`
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
If tan θ – sin2θ = cos2θ, then show that `sin^2θ = 1/2`.
