Advertisements
Advertisements
प्रश्न
If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =
पर्याय
a2 b2
ab
a4 b4
a2 + b2
Advertisements
उत्तर
Given:
`x= a cosθ, y= b sin θ`
So,
`b^2 x^2+a^2 y^2`
= `b^2(a cos)^2+a^2(b sin θ)^2`
=` b^2 a^2 cos^2θ+a^2 b^2 sin^2θ`
=`b^2a^2 (cos^2 θ+sin^2θ)`
We know that,
`sin^2θ+cos^2θ=1`
Therefore,` 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-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec2 A = 1 cot2 A.
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Prove the following identities:
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
Write the value of tan1° tan 2° ........ tan 89° .
If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.
The value of sin2 29° + sin2 61° is
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
Prove that `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`
Prove that sec2 (90° - θ) + tan2 (90° - θ) = 1 + 2 cot2 θ.
Without using the trigonometric table, prove that
cos 1°cos 2°cos 3° ....cos 180° = 0.
Without using trigonometric table, prove that
`cos^2 26° + cos 64° sin 26° + (tan 36°)/(cot 54°) = 2`
If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
If 5 tan β = 4, then `(5 sin β - 2 cos β)/(5 sin β + 2 cos β)` = ______.
Prove that `(1 + tan^2 A)/(1 + cot^2 A)` = sec2 A – 1
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
