Question

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

Answer 1

0°

360°

Explanation:

We want to solve the equation,

`\cos(x + 45) + \cos(x - 45) = √(2)`

We expand using trigonometric identities to get;

`\cos(x) \cos( 45) - \sin(x) \sin(45) + \cos(x) \cos( 45) + \sin(x) \sin(45) = √(2)`

`( √(2) )/(2) \cos(x) - ( √(2) )/(2) \sin(x) + ( √(2) )/(2) \cos(x) + ( √(2) )/(2) \sin(x) = √(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`