Question

what are the possible values of x?
`( \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}`