4sin^2 = cos x + 3
4(1-cos^2) = cos + 3
-4cos^2 -cos x +1
4cos^2 + cos x - 1
I was thinking of using quadratic formula as I tried to factor
Product -4
Sum 1
or
cos x (4 cos x + 1) -1 *I don't know what to do since it is = to -cos x / cos x
4sin^2 = cos x + 3
4(1-cos^2) = cos + 3
-4cos^2 -cos x +1
4cos^2 + cos x - 1
I was thinking of using quadratic formula as I tried to factor
Product -4
Sum 1
or
cos x (4 cos x + 1) -1 *I don't know what to do since it is = to -cos x / cos x
This is not an identity, it is an equation. And you didn't even consistently put in the argument of the functions! "cos " is meaningless in this situation without the argument.
$\displaystyle 4sin^2(x) = cos(x) + 3$
Now, $\displaystyle sin^2(x) + cos^2(x) = 1$, so we have
$\displaystyle 4(1 - cos^2(x)) = cos(x) + 3$
$\displaystyle 4 - 4cos^2(x) = cos(x) + 3$
$\displaystyle 4cos^2(x) + cos(x) - 1 = 0$
Now let $\displaystyle y = cos(x)$:
$\displaystyle 4y^2 + y - 1 = 0$
The quadratic formula says that
$\displaystyle y = \frac{-1 \pm \sqrt{17}}{8}$
Thus
$\displaystyle cos(x) = \frac{-1 \pm \sqrt{17}}{8}$
So
$\displaystyle x = cos^{-1} \left ( \frac{-1 \pm \sqrt{17}}{8} \right )$
You can do both of them on your calculator. I leave the rest to you.
-Dan