Advertisements
Advertisements
प्रश्न
If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =
पर्याय
ab
a2 − b2
a2 + b2
a2 b2
Advertisements
उत्तर
Given:
`x= a secθ, y=b tanθ`
So,
`b^2x^2-a^2 y^2`
=` b^2(a secθ)^2-a^2(btan θ)^2`
= `b^2 a^2 sec^2 θ-a^2 b^2 tan^2θ`
=` b^2 a^2 (sec^2θ-tan^2 θ)`
We know that,`
`sec^2θ-tan^2θ=1`
Therfore,
`b^2x^2-a^2y^2=a^2b^2`
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
Prove the following trigonometric identities.
sec A (1 − sin A) (sec A + tan A) = 1
Prove the following trigonometric identities.
`(sec A - tan A)/(sec A + tan A) = (cos^2 A)/(1 + sin A)^2`
Prove the following identities:
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
`cot^2 theta - 1/(sin^2 theta ) = -1`a
`(sec theta + tan theta )/( sec theta - tan theta ) = ( sec theta + tan theta )^2 = 1+2 tan^2 theta + 25 sec theta tan theta `
If `(cosec theta - sin theta )= a^3 and (sec theta - cos theta ) = b^3 , " prove that " a^2 b^2 ( a^2+ b^2 ) =1`
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Prove the following identity :
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
Prove the following identity :
`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
If sec θ = `41/40`, then find values of sin θ, cot θ, cosec θ
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
Show that: `tan "A"/(1 + tan^2 "A")^2 + cot "A"/(1 + cot^2 "A")^2 = sin"A" xx cos"A"`
(sec2 θ – 1) (cosec2 θ – 1) is equal to ______.
