SOLUTION: Solve for the solution over the domain: -180 < or equal to x < or equal to 360 degrees. Equation is : 2= sq.root2 cos((1/2)(x-30degrees)) +1

 

Subtract 1 from both sides:



Divide both sides by √2



Use the half-angle formula:  

 

Square both sides:

 

Multiply both sides by 2:



Subtract 1 from both sides of the equation:







Add 30o to both sides



Since we are given:





We subtract 120o from all three sides



Divide all three sides by 180°







Since n must be an integer,



So n = -1, 0, 1

Since

,

For n = -1




For n = 0




For n = 1




However, we squared both sides and that means that there may be
one or more extraneous solutions.

If we check each one using a calculator, we find that 300° is
not a solution and that there are only two solutions,

-60° and 120° 

Edwin

I realized there was a simpler solution without extraneous solutions:

 

Subtract 1 from both sides:



Divide both sides by √2







Multiply both sides by 2



Add 30° to both sides



Since we are given:





We subtract 30° from all three sides



We subtract or add 90° from/to all three sides:



Divide all three sides by 720°





Using the +





Since n is an integer, n=0





Using the -





Since n is an integer, n=0





There are two solutions:

-60° and 120° 

Edwin