MHT CET · Maths · Trigonometric Ratios & Identities
If \(x=3 \sin \theta, y=3 \cos \theta \cos \phi, z=3 \cos \theta \sin \emptyset\), then \(x^{2}+y^{2}+z^{2}=\)
- A \(18\)
- B \(27\)
- C \(9\)
- D \(3\)
Answer & Solution
Correct Answer
(C) \(9\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} x^{2}+y^{2}+z^{2} &=9 \sin ^{2} \theta+9 \cos ^{2} \theta \cos ^{2} \phi+9 \cos ^{2} \theta \sin ^{2} \phi \\ &=9 \sin ^{2} \theta+9 \cos ^{2} \theta\left(\cos ^{2} \phi+\sin ^{2} \phi\right) \\ &=9 \sin ^{2} \theta+9 \cos ^{2} \theta \\ &=9\left(\sin ^{2} \theta+\cos ^{2} \theta\right)=9 \times 1=9 \end{aligned}\)
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