Trigonometry Examples

$1 + \cos (2 x) = \cot (x) \sin (x)$

Step 1

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 1.1

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

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

Step 1.2

Cancel the common factors.

$1 + \cos (2 x) = \cos (x)$

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