Step-by-step explanation:
[tex]cos(x + 45 \degree) + cos(x - 45 \degree) = \sqrt{2} \\ cosx \: cos45 \degree - sinx \: sin45 \degree \\ + cosx \: cos45 \degree + sinx \: sin45 \degree = \sqrt{2} \\ 2cosx \: cos45 \degree = \sqrt{2} \\ 2cosx \times \frac{1}{ \sqrt{2} } = \sqrt{2} \\ 2cosx = \sqrt{2} \times \sqrt{2} \\ 2cosx = 2 \\ cosx = \frac{2}{2} \\ cosx = 1 \\ cosx = cos \: 0 \degree \\ \huge \red{ \boxed{ x = 0 \degree}} \\ [/tex]
