Search any question & find its solution
Question:
Answered & Verified by Expert
\( \int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d x \) is equal to
Options:
Solution:
2001 Upvotes
Verified Answer
The correct answer is:
\( 2(\sin x+x \cos \theta)+C \)
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,
$\int \frac{\left(2 \cos ^{2} x-1\right)-\left(2 \cos ^{2} \theta-1\right)}{\cos x-\cos \theta} d x$
$=2 \int(\cos x+\cos \theta) d x=2(\sin x+x \cos \theta)+C$
Since, $\cos 2 \theta=2 \cos ^{2} \theta 1$ So,
$\int \frac{\left(2 \cos ^{2} x-1\right)-\left(2 \cos ^{2} \theta-1\right)}{\cos x-\cos \theta} d x$
$=2 \int(\cos x+\cos \theta) d x=2(\sin x+x \cos \theta)+C$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.