Trigonometry Examples

$- 2 \sin^{2} (x) - 2 \cos (x) + 2 = \cos (x) - 1$

Step 1

Simplify $- 2 \sin^{2} (x) - 2 \cos (x) + 2$ .

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Step 1.1

Simplify with factoring out.

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Step 1.1.1

Move $2$ .

$- 2 \sin^{2} (x) + 2 - 2 \cos (x) = \cos (x) - 1$

Step 1.1.2

Reorder $- 2 \sin^{2} (x)$ and $2$ .

$2 - 2 \sin^{2} (x) - 2 \cos (x) = \cos (x) - 1$

Step 1.1.3

Factor $2$ out of $2$ .

$2 (1) - 2 \sin^{2} (x) - 2 \cos (x) = \cos (x) - 1$

Step 1.1.4

Factor $2$ out of $- 2 \sin^{2} (x)$ .

$2 (1) + 2 (- \sin^{2} (x)) - 2 \cos (x) = \cos (x) - 1$

Step 1.1.5

Factor $2$ out of $2 (1) + 2 (- \sin^{2} (x))$ .

$2 (1 - \sin^{2} (x)) - 2 \cos (x) = \cos (x) - 1$

Step 1.2

Apply pythagorean identity.

$2 \cos^{2} (x) - 2 \cos (x) = \cos (x) - 1$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 2 π n, \frac{π}{3} + 2 π n, \frac{5 π}{3} + 2 π n$ , for any integer $n$

Step 3