Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If $x+y+z=180^{\circ}$, then $\cos 2 x+\cos 2 y-\cos 2 z$ is equal to
MathematicsTrigonometric EquationsJEE Main
Options:
  • A $4 \sin x \cdot \sin y \cdot \sin z$
  • B $1-4 \sin x \cdot \sin y \cdot \cos z$
  • C $4 \sin x \cdot \sin y \cdot \sin z-1$
  • D $\cos A \cdot \cos B \cdot \cos C$
Solution:
1647 Upvotes Verified Answer
The correct answer is: $1-4 \sin x \cdot \sin y \cdot \cos z$
$\begin{aligned} & \cos 2 x+\cos 2 y-\cos 2 z \\ & =2 \cos (x+y) \cos (x-y)-2 \cos ^2 z+1 \\ & =2 \cos (\pi-z) \cos (x-y)-2 \cos ^2 z+1 \\ & =1-2 \cos z\{\cos (x-y)-\cos (x+y)\} \\ & =1-2 \cos z 2 \sin x \sin y=1-4 \sin x \sin y \cos z\end{aligned}$

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.