Trigonometry Examples

$\tan (x) - 2 \cos (x) \tan (x) = 0$

Step 1

Simplify $\tan (x) - 2 \cos (x) \tan (x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

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

Step 1.1.2

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

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Step 1.1.2.1

Add parentheses.

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

Step 1.1.2.2

Reorder $\cos (x)$ and $\tan (x)$ .

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

Step 1.1.2.3

Rewrite $- 2 \cos (x) \tan (x)$ in terms of sines and cosines.

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

Step 1.1.2.4

Cancel the common factors.

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

Step 1.2

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$\tan (x) - 2 \sin (x) = 0$

Step 2

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

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

Step 3