Q80 / 155 · WBJEE 2024 · Mathematics

The expression $\cos ^2 \phi+\cos ^2(\theta+\phi)-2 \cos \theta \cos \phi \cos (\theta+\phi)$ is

  • A
    independent of $\theta$
  • Correct answer
    B
    independent of $\phi$
  • C
    independent of $\theta$ and $\phi$
  • D
    dependent on $\theta$ and $\phi$

Solution

$\begin{aligned} & \text { Hint: } \cos ^2 \phi+\cos ^2(\theta+\phi)-2 \cos \theta \cdot \cos \phi \cos (\theta+\phi) \\ & \text { for } \theta=0 \\ & \cos ^2 \phi+\cos ^2 \phi-2 \cos ^2 \phi=0 \end{aligned}$ $\text {which is independent from } \phi \text {. }$

Hence, the correct answer is option: 'B'.

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