Advertisements
Advertisements
प्रश्न
Prove the following identity :
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
Advertisements
उत्तर
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
`(1 + cosA)/sinA + sinA/(1 + cosA)`
= `((1 + cosA)^2 + sin^2A)/(sinA(1 + cosA))`
= `(1 + 2cosA + cos^2A + sin^2A)/(sinA(1 + cosA))`
= `(2 + 2cosA)/(sinA(1 + cosA))`
= `(2(1 + cosA))/(sinA(1 + cosA)` [`sin^2A + cos^2A = 1`]
= 2 cosec A
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`sin theta/(1 - cos theta) = cosec theta + cot theta`
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
Prove the following identity :
`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`
Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°.
If tan α = n tan β, sin α = m sin β, prove that cos2 α = `(m^2 - 1)/(n^2 - 1)`.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
Prove that `1/("cosec" θ - cot θ) = "cosec" θ + cot θ`.
Prove that sin4A – cos4A = 1 – 2 cos2A.
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
