If x = r cos θ cos φ, y = r cos θ sin φ and z = r sin θ, then the value of x² + y² + z² is
Answer : Option A
Explanation : x = r cosθ . cosφ
y = r cos sinφ
z = r sinθ
z = r sin
∴ x2 + y2 + z2 = r2 cos2θ. cos2φ + r2cos2θ . sin2φ+
r2 sin2θ
= r2cos2θ(cos2φ + sin2φ) + r2 sin2θ
= r2cos2θ+r2φsin2θ
= r2 (cos2θ+ sin2θ) = r2
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