Advertisements
Advertisements
प्रश्न
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
Advertisements
उत्तर
We have,
x = r sin θ cos Φ,
y = r sin θ sin Φ,
z = r cos θ
Squaring and adding,
x2 + y2 + z2
= r2 sin2θ cos2Φ + r2 sin2θ sin2Φ + r2 cos2θ
= r2 sin2θ (cos2Φ + sin2Φ) + r2 cos2θ
= r2 sin2θ x (1) + r2 cos2θ
= r2 (sin2θ + cos2θ)
= r2 x 1 = r2
Hence, x2 + y2 + z2 = r2.
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 + cos A)/sin^2 A = 1/(1 - cos A)`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
Write the value of tan1° tan 2° ........ tan 89° .
Find the value of sin ` 48° sec 42° + cos 48° cosec 42°`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
Prove that sec2θ – cos2θ = tan2θ + sin2θ.
Eliminate θ if x = r cosθ and y = r sinθ.
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
Prove the following trigonometry identity:
(sin θ + cos θ)(cosec θ – sec θ) = cosec θ ⋅ sec θ – 2 tan θ
