# Math Help - Solving Identities

1. ## Solving Identities

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

2. Originally Posted by Quan
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.

$4sin^2(x) = cos(x) + 3$

Now, $sin^2(x) + cos^2(x) = 1$, so we have
$4(1 - cos^2(x)) = cos(x) + 3$

$4 - 4cos^2(x) = cos(x) + 3$

$4cos^2(x) + cos(x) - 1 = 0$

Now let $y = cos(x)$:
$4y^2 + y - 1 = 0$

$y = \frac{-1 \pm \sqrt{17}}{8}$
$cos(x) = \frac{-1 \pm \sqrt{17}}{8}$
$x = cos^{-1} \left ( \frac{-1 \pm \sqrt{17}}{8} \right )$