Question

Solve each equation for 0≤x≤360 cos(x+45°)+cos(x-45°)= √2

Answer 1

Answer:

0°

360°

Step-by-step explanation:

We want to solve the equation,

$\cos(x + 45) + \cos(x - 45) = \sqrt{2}$

We expand using trigonometric identities to get;

$\cos(x) \cos( 45) - \sin(x) \sin(45) + \cos(x) \cos( 45) + \sin(x) \sin(45) = \sqrt{2}$

$\frac{ \sqrt{2} }{2} \cos(x) - \frac{ \sqrt{2} }{2} \sin(x) + \frac{ \sqrt{2} }{2} \cos(x) + \frac{ \sqrt{2} }{2} \sin(x) = \sqrt{2}$

Simplify;

$\cos(x) - \sin(x) + \cos(x) + \sin(x) = 2$

Simplify;

$\cos(x) + \cos(x) = 2$

Add

$2\cos(x) = 2$

Divide by 2

$\cos(x) = 1$

Take cosine inverse;

In the

$x = \cos^{ - 1} ( 1) =0\degree$

Also in the 3rd quadrant cosine ratio is positive.

$x = 360-0= 360 \degree$