WBJEE · Maths · Trigonometric Ratios & Identities
The expression \(\cos ^2 \phi+\cos ^2(\theta+\phi)-2 \cos \theta \cos \phi \cos (\theta+\phi)\) is
- A independent of \(\theta\)
- B independent of \(\phi\)
- C independent of \(\theta\) and \(\phi\)
- D dependent on \(\theta\) and \(\phi\)
Answer & Solution
Correct Answer
(B) independent of \(\phi\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Hint: } \cos ^2 \phi+\cos ^2(\theta+\phi)-2 \cos \theta \cdot \cos \phi \cos (\theta+\phi) \\ & \text { for } \theta=0 \\ & \cos ^2 \phi+\cos ^2 \phi-2 \cos ^2 \phi=0 \end{aligned}\) \(\text {which is independent from } \phi \text {. }\)
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