Advertisements
Advertisements
प्रश्न
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
Advertisements
उत्तर
`(b^2 x^2 + a^2 y^2)`
=`b^2 (a sin theta )^2 + a^2 ( bcos theta)^2`
=`b^2 a^2 sin^2 theta + a^2 b^2 cos^2 theta`
=`a^2 b^2 ( sin^2 theta + cos ^2 theta)`
=`a^2 b^2 (1)`
=`a^2 b^2`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1/(sec^2 theta - cos theta) + 1/(cosec^2 theta - sin^2 theta)) sin^2 theta cos^2 theta = (1 - sin^2 theta cos^2 theta)/(2 + sin^2 theta + cos^2 theta)`
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
Prove the following trigonometric identities.
if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1
If cos θ + cos2 θ = 1, prove that sin12 θ + 3 sin10 θ + 3 sin8 θ + sin6 θ + 2 sin4 θ + 2 sin2 θ − 2 = 1
If sec A + tan A = p, show that:
`sin A = (p^2 - 1)/(p^2 + 1)`
` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
Write the value of `4 tan^2 theta - 4/ cos^2 theta`
Prove that:
`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
Prove that `(tan θ + sin θ)/(tan θ - sin θ) = (sec θ + 1)/(sec θ - 1)`
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
Prove that `(tan(90 - theta) + cot(90 - theta))/("cosec" theta)` = sec θ
Prove that sin4A – cos4A = 1 – 2cos2A
Eliminate θ if x = r cosθ and y = r sinθ.
