Trigonometrical Equations 3 Question 14
15. 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……. .
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Answer:
Correct Answer: 15. No solution
Solution:
- 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.
