Trigonometrical Equations Ques 41

  1. 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: 41.No solution

Solution:

Formula:

Sum & Difference Identities:

  1. 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.



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