Question

what are the possible values of x?$\frac{ \cos(2x) }{ \cos(x) + \sin(x) } = 0$where $0 \leqslant x \leqslant 180$

Answer 1

Answer:$45\degree\text{ or 225}\degree$Explanations:

The given equation is:

$\frac{\cos 2x}{\cos x\text{ +sinx }}=\text{ 0}$

Cross multiply:

cos 2x = 0 ( cos x + sin x)

cos 2x = 0

$\begin{gathered} 2x\text{ = }\cos ^{-1}0 \\ \text{Note: }\cos ^{-1}0\text{ = 90}\degree\text{ or 450} \\ 2x\text{ = 90} \\ x\text{ = 90/2} \\ x\text{ = 45}\degree \\ \text{Also: 2x = 450} \\ \text{x = 450/}2 \\ x\text{ = 225} \end{gathered}$