Question

if x is equal to R sin theta cos Y equal to R sin theta sin Z = 2r cos theta prove that AC square equal to X square + Y square + Z Square​

Answer 1

Given: The values X = R x sinθ x cosΦ, Y = R x sinθ x sinΦ, Z = R x cosθ

To Find: Prove that  X² + Y² + Z² = R²

Solution:

• Now we have given the values:

            X = R x sinθ x cosΦ, Y = R x sinθ x sinΦ, Z = R x cosθ

• Squaring each term, we get:

            X² = R² x sin²θ x cos²Φ, Y² = R² x sin²θ x sin²Φ, Z² = R² x cos²θ

• Adding them all, we get:

            X² + Y² + Z² = R² x sin²θ x cos²Φ + R² x sin²θ x sin²Φ + R² x cos²θ

             X² + Y² + Z² = R² x sin²θ (cos²Φ + sin²Φ ) + R² x cos²θ

• Now we know that sin^2 x + cos^2 x = 1, so applying this, we get:

             X² + Y² + Z² = R² x sin²θ (1) + R² x cos²θ

• Taking R^2 common, we get:

             X² + Y² + Z² = R² x (sin²θ + cos²θ)

            X² + Y² + Z² = R² x 1

            X² + Y² + Z² = R²             Hence proved

Answer:

          So in solution part, we proved that X² + Y² + Z² = R²

Answer 2

solution is x²+y²+z²=r²