Search any question & find its solution
Question:
Answered & Verified by Expert
If $\cos x+\cos y=-\cos \alpha, \sin x+\sin y=-\sin \alpha$, then $\cot \left(\frac{x+y}{2}\right)=$
Options:
Solution:
1030 Upvotes
Verified Answer
The correct answer is:
$\cot \propto$
Given $\cos x+\cos y=-\cos \alpha$ and $\sin x+\sin y=-\sin \alpha$
$2 \cos \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right)=-\cos \alpha$ ...(1) and
$2 \sin \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right)=-\sin \alpha$ ...(2)
Divided equation (1) by equation (2)
$\cot \left(\frac{x+y}{2}\right)=\cot \alpha$
$2 \cos \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right)=-\cos \alpha$ ...(1) and
$2 \sin \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right)=-\sin \alpha$ ...(2)
Divided equation (1) by equation (2)
$\cot \left(\frac{x+y}{2}\right)=\cot \alpha$
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.