Question

The solutions of the system of equations $x+y=\frac{2\pi }{3}$ and
$cosx+cosy=\frac{3}{2}$ where x and y are real, are

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$G.E\Rightarrow 2cos\left(\frac{x+y}{2}\right)cos\left(\frac{x-y}{2}\right)=\frac{3}{2}\Rightarrow 2cos\left(\frac{\pi }{3}\right)cos\left(\frac{x-y}{2}\right)=\frac{3}{2}\Rightarrow 2.\frac{1}{2}.cos\left(\frac{x-y}{2}\right)=\frac{3}{2}\Rightarrow cos\left(\frac{x-y}{2}\right)=\frac{3}{2}$ >1
$\therefore$ Given equation has no solution.