Question

Evaluate: $\frac{\cos 3A-2\cos 4A}{\sin 3A+2\sin 4A}$, When $A={15}^o$

Answer 1

$\frac{\cos 3A-2\cos 4A}{\sin 3A+2\sin 4A}$ & $A={15}^o$

$\frac{\cos {45}^o-2\cos {60}^o}{\sin {45}^o+2\sin {60}^o}=\frac{1/\sqrt{2}-2\times 1/2}{1/\sqrt{2}+2\times \sqrt{3}/2}$

$=\frac{1/\sqrt{2}-1}{1/\sqrt{2}+\sqrt{3}}$

$\Rightarrow \frac{1-\sqrt{2}}{1+\sqrt{6}}$.