Trigonometry Examples

$\sqrt{3} \sin (x) \sec (x) = 2 \sin (x)$

Step 1

Simplify $\sqrt{3} \sin (x) \sec (x)$ .

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Step 1.1

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

$\sqrt{3} \sin (x) \frac{1}{\cos (x)} = 2 \sin (x)$

Step 1.2

Multiply $\sqrt{3} \sin (x) \frac{1}{\cos (x)}$ .

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Step 1.2.1

Combine $\frac{1}{\cos (x)}$ and $\sqrt{3}$ .

$\frac{\sqrt{3}}{\cos (x)} \sin (x) = 2 \sin (x)$

Step 1.2.2

Combine $\frac{\sqrt{3}}{\cos (x)}$ and $\sin (x)$ .

$\frac{\sqrt{3} \sin (x)}{\cos (x)} = 2 \sin (x)$

Step 1.3

Separate fractions.

$\frac{\sqrt{3}}{1} \cdot \frac{\sin (x)}{\cos (x)} = 2 \sin (x)$

Step 1.4

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

$\frac{\sqrt{3}}{1} \tan (x) = 2 \sin (x)$

Step 1.5

Divide $\sqrt{3}$ by $1$ .

$\sqrt{3} \tan (x) = 2 \sin (x)$

Step 2

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

$x = 2 π n, \frac{π}{6} + 2 π n, π + 2 π n, \frac{11 π}{6} + 2 π n$ , for any integer $n$

Step 3