SOLUTION: If x = r sin A cos B and y = r sin A sin B and z = r cos A ,verify x^2 + y^2 + z^2 = r^2. Can you please help me?Thanks so much in advance:)

Question 826147: If x = r sin A cos B and y = r sin A sin B and z = r cos A ,verify x^2 + y^2 + z^2 = r^2.
Can you please help me?Thanks so much in advance:)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
What we're going to do is take:

and substitute in the given expressions for x, y and z. Then we will use algebra and/or trig properties to transform the expression into .

Substituting in the given expressions:

Squaring each expression:

Factor out :

Now, if we can find a way to turn the second factor into a 1, we will be finished! Factoring out of the first two terms in the second factor:

Since this becomes:

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