Q98 / 180 · KCET 2017 · Mathematics

\( \int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d x \) is equal to

  • Correct answer
    A
    \( 2(\sin x+x \cos \theta)+C \)
  • B
    \( 2(\sin x-x \cos \theta)+C \)
  • C
    \( 2(\sin x+2 x \cos \theta)+C \)
  • D
    \( 2(\sin x-2 x \cos \theta)+C \)

Solution

Given that, $\int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d$ Since, $\cos 2 \theta=2 \cos ^{2} \theta 1$ So, $\int \frac{\left(2 \cos ^{2} x-1\right)-\left(2 \cos ^{2} \theta-1\right)}{\cos x-\cos \theta} d x$ $=2 \int(\cos x+\cos \theta) d x=2(\sin x+x \cos \theta)+C$

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

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