solve for x: 4cos 2x + 3

[xomandi]

here is what i did
4cos 2x + 3
4 cos 2x = -3
cos 2x = -3/4

i think the identity is 1 + cos^2 x/2 but then what do i do to solve for x??

 

[tkhunny]

There are some very difficult notation problems on this one.

First, solve what? You have not provided an equation. From your second step, I see that you intended an equation. It is not the same if you fail to write "=0". That's what makes it an equation.

Second, you seem to be on the right track, but please think about what you are writing. Here is what you have written: $\displaystyle 1\;+\;\cos^{2}{\frac{x}{2}}$. Is that what you mean? I believe it is not. Perhaps you meant: $\displaystyle 1\;+\;\frac{\cos^{2}{x}}{2}$? Maybe $\displaystyle \frac{1\;+\;\cos^{2}{x}}{2}$. If you did mean one of those, what is it for? Again, you have not provided an equation.

Since $\displaystyle \cos{2x}\;=\;2\cos^{2}{x}\;-\;1$, we have $\displaystyle \cos{x}\;=\;\sqrt{\frac{(\cos{2x})+1}{2}}$ without consideration of the Quadrant of either.

Okay, where does that leave us?

Note: PLEASE be more careful with your notation. Make sure what you write is what you mean.