Trigonometry Examples

$2 \cos^{2} (x) + 2 \sin^{2} (\frac{x}{2}) - 1 = 0$

Step 1

Simplify $2 \cos^{2} (x) + 2 \sin^{2} (\frac{x}{2}) - 1$ .

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Step 1.1

Move $- 1$ .

$2 \cos^{2} (x) - 1 + 2 \sin^{2} (\frac{x}{2}) = 0$

Step 1.2

Apply the cosine double-angle identity.

$\cos (2 x) + 2 \sin^{2} (\frac{x}{2}) = 0$

Step 2

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

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

Step 3