Trigonometry Examples

$(\tan (x + \sqrt{3})) (2 \sin (x - 1)) = 0$

Step 1

Simplify $(\tan (x + \sqrt{3})) (2 \sin (x - 1))$ .

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Step 1.1

Rewrite using the commutative property of multiplication.

$2 \tan (x + \sqrt{3}) \sin (x - 1) = 0$

Step 1.2

Rewrite $\tan (x + \sqrt{3})$ in terms of sines and cosines.

$2 \frac{\sin (x + \sqrt{3})}{\cos (x + \sqrt{3})} \sin (x - 1) = 0$

Step 1.3

Combine $2$ and $\frac{\sin (x + \sqrt{3})}{\cos (x + \sqrt{3})}$ .

$\frac{2 \sin (x + \sqrt{3})}{\cos (x + \sqrt{3})} \sin (x - 1) = 0$

Step 1.4

Combine $\frac{2 \sin (x + \sqrt{3})}{\cos (x + \sqrt{3})}$ and $\sin (x - 1)$ .

$\frac{2 \sin (x + \sqrt{3}) \sin (x - 1)}{\cos (x + \sqrt{3})} = 0$

Step 1.5

Separate fractions.

$\frac{2 \sin (x - 1)}{1} \cdot \frac{\sin (x + \sqrt{3})}{\cos (x + \sqrt{3})} = 0$

Step 1.6

Convert from $\frac{\sin (x + \sqrt{3})}{\cos (x + \sqrt{3})}$ to $\tan (x + \sqrt{3})$ .

$\frac{2 \sin (x - 1)}{1} \tan (x + \sqrt{3}) = 0$

Step 1.7

Divide $2 \sin (x - 1)$ by $1$ .

$2 \sin (x - 1) \tan (x + \sqrt{3}) = 0$

Step 2

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

$x \approx 1 + π n, 1.40954184 + π n$ , for any integer $n$

Step 3