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:
`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`
[Hint: Write the expression in terms of sinθ and cosθ]
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
Prove the following trigonometric identities.
`"cosec" theta sqrt(1 - cos^2 theta) = 1`
Prove the following trigonometric identities.
`1/(sec A - 1) + 1/(sec A + 1) = 2 cosec A cot A`
Prove the following trigonometric identities.
`tan A/(1 + tan^2 A)^2 + cot A/((1 + cot^2 A)) = sin A cos A`
Prove the following identities:
`(1 + sin A)/(1 - sin A) = (cosec A + 1)/(cosec A - 1)`
Prove the following identities:
`1 - cos^2A/(1 + sinA) = sinA`
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
Prove that
`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
If `cos theta/(1 + sin theta) = 1/"a"`, then prove that `("a"^2 - 1)/("a"^2 + 1)` = sin θ
Choose the correct alternative:
cos 45° = ?
Prove that `(cos^2theta)/(sintheta) + sintheta` = cosec θ
Prove that 2(sin6A + cos6A) – 3(sin4A + cos4A) + 1 = 0
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
