Trigonometry Examples

$2 \cot^{2} (x) \sin^{2} (x) - \cos (x) = 0$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\cot (x)$ in terms of sines and cosines.

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

Step 1.2

Apply the product rule to $\frac{\cos (x)}{\sin (x)}$ .

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

Step 1.3

Combine $2$ and $\frac{\cos^{2} (x)}{\sin^{2} (x)}$ .

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

Step 1.4

Cancel the common factor of $\sin^{2} (x)$ .

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Step 1.4.1

Cancel the common factor.

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

Step 1.4.2

Rewrite the expression.

$2 \cos^{2} (x) - \cos (x) = 0$

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