Answer:
0°
360°
Step-by-step explanation:
We want to solve the equation,
[tex] \cos(x + 45) + \cos(x - 45) = \sqrt{2} [/tex]
We expand using trigonometric identities to get;
[tex]\cos(x) \cos( 45) - \sin(x) \sin(45) + \cos(x) \cos( 45) + \sin(x) \sin(45) = \sqrt{2} [/tex]
[tex] \frac{ \sqrt{2} }{2} \cos(x) - \frac{ \sqrt{2} }{2} \sin(x) + \frac{ \sqrt{2} }{2} \cos(x) + \frac{ \sqrt{2} }{2} \sin(x) = \sqrt{2} [/tex]
Simplify;
[tex] \cos(x) - \sin(x) + \cos(x) + \sin(x) = 2[/tex]
Simplify;
[tex]\cos(x) + \cos(x) = 2[/tex]
Add
[tex]2\cos(x) = 2[/tex]
Divide by 2
[tex]\cos(x) = 1[/tex]
Take cosine inverse;
In the
[tex]x = \cos^{ - 1} ( 1) =0\degree [/tex]
Also in the 3rd quadrant cosine ratio is positive.
[tex]x = 360-0= 360 \degree[/tex]
