Advertisements
Advertisements
प्रश्न
Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`
Advertisements
उत्तर
`L.H.S = sqrt((1-cosA)/(1 + cosA))`
`= sqrt(((1-cosA)(1 + cosA))/((1+ cosA)(1 + cosA)))`
`= sqrt((1 - cos^2A)/(1 + cosA)^2`
`= sqrt((sin^2A)/(1+cosA)^2)`
`= sinA/(1 + cosA)`
= R.H.S
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 + cos θ + sin θ)/(1 + cos θ - sin θ) = (1 + sin θ)/cos θ`
Prove the following identities:
cosec4 A – cosec2 A = cot4 A + cot2 A
Prove the following identities:
(1 + tan A + sec A) (1 + cot A – cosec A) = 2
If sec A + tan A = p, show that:
`sin A = (p^2 - 1)/(p^2 + 1)`
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Without using a trigonometric table, prove that
`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.
Prove that: sin6θ + cos6θ = 1 - 3sin2θ cos2θ.
Prove that `sqrt((1 + cos A)/(1 - cos A)) = "cosec" A + cot A`.
Show that tan 7° × tan 23° × tan 60° × tan 67° × tan 83° = `sqrt(3)`.
