Trigonometrical Equations Ques 41
- The solution set of the system of equations $x+y=\frac{2 \pi}{3}, \cos x+\cos y=\frac{3}{2}$, where $x$ and $y$ are real, is……. .
Show Answer
Answer:
Correct Answer: 41.No solution
Solution:
Formula:
- Given, $x+y=\frac{2 \pi}{3}$
and $\quad \cos x+\cos y=\frac{3}{2}$
$\Rightarrow \cos x+\cos (\frac{2 \pi}{3}-x)=\frac{3}{2}$
$\Rightarrow \quad \cos x+(-\frac{1}{2} \cos x+\frac{\sqrt{3}}{2} \sin x)=\frac{3}{2}$
$\Rightarrow \quad \frac{1}{2} \cos x+\frac{\sqrt{3}}{2} \sin x=\frac{3}{2}$
$\Rightarrow \quad \sin (\frac{\pi}{6}+x)=\frac{3}{2}$, which is never possible.
Hence, no solution exists.
BETA
