Advertisements
Advertisements
प्रश्न
Prove the following identity :
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
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
`((1 + sin theta)^2 + (1 + sin theta)^2)/(2cos^2 theta) = (1 + sin^2 theta)/(1 - sin^2 theta)`
Prove the following trigonometric identities.
if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1
Prove the following identities:
`1/(tan A + cot A) = cos A sin A`
Prove the following identities:
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`
Prove the following identities:
`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
If cosθ = `5/13`, then find sinθ.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
Prove that cot2θ × sec2θ = cot2θ + 1
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
