If x = a cos θ cos θ, y = a cosθ sinθ

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If x = a cos θ cos θ, y = a cosθ sinθ and z = a sinθ, then the value of (x² + y² + z²) is

1. 2a²
2. 4a²
3. 9a²
4. a²

Correct Option: D

x = a cosθ. cosφ
y = a cosθ. sinφ
z = a sinθ
∴ x² + y² + z²
= a²cos². cos²θ + a²cos².sin²φ + a²sin²θ
= a²cos²θ(cos²φ + sin²φ) + a²sin²θ
= a²cos²θ + a²sin²θ
= a²(cos²θ + sin²θ) = a²