Advertisements
Advertisements
प्रश्न
Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`
Advertisements
उत्तर
`sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta))`
`= sqrt((1 + cos theta)/(1 - cos theta) xx (1 + cos theta)/(1 + cos theta)) + sqrt((1 -cos theta)/(1 + cos theta) xx (1 - cos theta)/(1 - cos theta))`
`= sqrt((1 + cos theta)^2/(1 - cos^2 theta)) + sqrt((1 - cos theta)^2/(1 - cos^2 theta))`
`= sqrt((1 + cos theta)^2/(sin^2 theta)) + sqrt((1 -cos theta)^2/sin^2 theta)`
`= (1 + cos theta)/sin theta + (1 - cos theta)/sin theta`
`= 2/sin theta = 2cosec theta`
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ`
`(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2`
`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`
Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
Prove the following trigonometric identities.
`(tan^2 A)/(1 + tan^2 A) + (cot^2 A)/(1 + cot^2 A) = 1`
Prove the following trigonometric identities
If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2
Prove the following trigonometric identities.
if x = a cos^3 theta, y = b sin^3 theta` " prove that " `(x/a)^(2/3) + (y/b)^(2/3) = 1`
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
Prove the following identities:
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2A * cos^2B)`
`(cot ^theta)/((cosec theta+1)) + ((cosec theta + 1))/cot theta = 2 sec theta`
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 :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`
If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
If x = a tan θ and y = b sec θ then
cos θ . sec θ = ?
(sec θ + tan θ) . (sec θ – tan θ) = ?
If 3 sin A + 5 cos A = 5, then show that 5 sin A – 3 cos A = ± 3.
If cos A + cos2A = 1, then sin2A + sin4A = ?
