Question

Solve:
$\frac{\cos {135}^o-\cos {120}^o}{\cos {135}^o+\cos {120}^o}=(3-2\sqrt{2})$

Answer 1

Consider the following differential eq.

$\frac{cos{135}^0-cos{120}^0}{cos{135}^0+cos{120}^0}$

$=\frac{cos({180}^0-{45}^0)-cos({180}^0-{60}^0)}{cos({180}^0-{45}^0)+cos({180}^0-{60}^0)}$

$=\frac{-\cos {45}^0+\cos {60}^0}{-\cos {45}^0-\cos {60}^0}$

$=\frac{-(\frac{1}{\sqrt{2}}-\frac{1}{2})}{-(\frac{1}{\sqrt{2}}+\frac{1}{2})}$

$=\frac{2-\sqrt{2}}{2+\sqrt{2}}$

$=\frac{{(2-\sqrt{2})}^2}{(2+\sqrt{2})(2-\sqrt{2})}$

$=(3-2\sqrt{2})$

Hence, this is the required answer.