Advertisements
Advertisements
प्रश्न
Prove the following identity:
`cosA/(1 + sinA) = secA - tanA`
Advertisements
उत्तर
LHS = `cosA/(1 + sinA)`
RHS = secA - tanA
= `1/cosA - sinA/cosA = (1 - sinA)/cosA`
= `(1 - sinA)/cosA((1 + sinA)/(1 + sinA)) = ((1 - sin^2A)/(cosA(1 + sinA)))`
= `cos^2A/(cosA(1 + sinA)) = cosA/((1 + sinA) ` = LHS
LHS = RHS
`cos A/(1+sinA) = secA - tanA`
APPEARS IN
संबंधित प्रश्न
Express the ratios cos A, tan A and sec A in terms of sin A.
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
if `x/a cos theta + y/b sin theta = 1` and `x/a sin theta - y/b cos theta = 1` prove that `x^2/a^2 + y^2/b^2 = 2`
Prove the following trigonometric identities.
if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1
`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`
The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]
Without using a trigonometric table, prove that
`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.
Prove the following identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`
Eliminate θ if x = r cosθ and y = r sinθ.
