cos^2x+3cos^2x+2=0 How do you solve this?
cos^2 x + 3 cos^2 x+2=0
4 cos^2 x = -2
cos^2 x = -1/2
cos x = plus or minus -1/2
x lies in the 1st, 2nd, 3rd and 4th quadrant since it has positive and negative values. Now find the basic angle $\displaystyle \alpha$ and solve for the 4 possible angles.
That's not true, if the equation was:
$\displaystyle \cos^2(x)=\frac{1}{4}$
Then you were right, because then:
$\displaystyle \cos(x)=\pm \frac{1}{2}$
Also, look at the graph of the function $\displaystyle 4\cos^2(x)+2$:
http://www.wolframalpha.com/input/?i=4cos^2%28x%29%2B2
What do you notice?