If ` x=r sin alpha cos beta, y= r sin alpha sin beta and z= r cos alpha , ` prove that
` x^(2)+y^(2) + z^(2) = r^(2). `

Explanation

To prove that \( x^2 + y^2 + z^2 = r^2 \) given the equations \( x = r \sin \alpha \cos \beta \), \( y = r \sin \alpha \sin \beta \), and \( z = r \cos \alpha \), we will follow these steps:

### Step 1: Write down the expressions for \( x \), \( y \), and \( z \)
We start with the given equations:
\[ x = r \sin \alpha \cos \beta \]
\[
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