2021 · Q55
If x = p sinA cosB, y = p sinA sinB and z = p cosA, then what is the value of x² + y² + z² ?
Elementary MathematicsTrigonometry
- A−p²
- B0
- Cp²
- D2p²
Explanation
x² + y² = p²sin²A(cos²B + sin²B) = p²sin²A, and adding z² = p²cos²A gives p²(sin²A + cos²A) = p². This is option (c).