Question

If x = r sin A cos B, y = r sin A sin B and
z = r cos A, then prove that:
x² + y² + z² = r²​

Answer 1

Answer:

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Answer 2

Answer:

Given:

• x = r sin A cos B
• y = r sin A sin B
• z = r cos A

To prove:

• x²+y²+z²=r²

Proof:

L.H.S.=

>> x²+y²+z²

• Putting values of x, y and z

>> (r sin A cos A)²+(r sin A sin B)²+(r cos A)²

>> r² sin²A cos²B + r² sin²A sin²B + r² cos²A

>> r² sin²A(cos²B + sin² B) + r² cos²A

• But, sin²Ø+cos²Ø=1

>> r² sin²A + r² cos²A

>> r²( sin²A + cos²A)

>> r²

>> R.H.S.

Hence, proved.