Question

I solved 2 cos(2x)+3=2 using inverse and then solved the same equation using the double angle formula, why are the answers different? what is the correct method?

Answer 1

When I use the inverse I get 60 and 120 degrees
When I use the cos (2x) double angle formula, I get 60 120 240 and 300
When I check with the TI83 I got 4 answers 60 120 240 and 300

Answer 2

You could even find an infinite number of solutions.
You use degrees. Does that imply your solutions have to be between 0 and 360?

Answer 3

You found 2x = 120, or 2x = 240, so x = 60 or x = 120 (divide by 2).
But: Every time you add 360, you've got a solution again, so the original solutions were actually:

2x = 120 + k*360, or 2x = 240 + k*360, where k is an integer.
Again, to find x, divide by 2:
x = 60 + k * 180 or x = 120 + k*180.

If x has to stay in the interval [0, 360], you have solutions: 60, 120, 240, 300.