First slide

Trigonometric Identities

Question

If $x = r \cos θ \cos ϕ, y = r c o s θ s i n ϕ, z = r \sin θ$ , then $x^{2} + y^{2} + z^{2} =$

Moderate

A

$r^{2}$
B

$y^{2}$
C

$x^{2}$
D

$z^{2}$

Solution

$x^{2} + y^{2} + z^{2} = r^{2} (\cos^{2} θ (\cos^{2} φ + \sin^{2} φ) + \sin^{2} θ)$

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