Advertisements
Advertisements
Question
If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x2 + y2 + z2 = r2
Advertisements
Solution
L.H.S. = x2 + y2 + z2
= (r sin A cos B)2 + (r sin A sin B)2 + (r cos A)2
= r2 sin2 A cos2 B + r2 sin2 A sin2 B + r2 cos2 A
= r2 sin2 A (cos2 B + sin2 B) + r2 cos2 A
= r2 (sin2 A + cos2 A)
= r2 = R.H.S.
APPEARS IN
RELATED QUESTIONS
`(cos theta cosec theta - sin theta sec theta )/(costheta + sin theta) = cosec theta - sec theta`
If `secθ = 25/7 ` then find tanθ.
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
For ΔABC , prove that :
`sin((A + B)/2) = cos"C/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")`
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
Prove that sec2θ – cos2θ = tan2θ + sin2θ.
If 2sin2θ – cos2θ = 2, then find the value of θ.
