Trigonometry Examples

$2 \sin (x) \cot (x) - \cot (x) = 2 \sin (x) - 1$

Step 1

Simplify $2 \sin (x) \cot (x) - \cot (x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

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Step 1.1.1.1

Add parentheses.

$2 (\sin (x) \cot (x)) - \cot (x) = 2 \sin (x) - 1$

Step 1.1.1.2

Reorder $\sin (x)$ and $\cot (x)$ .

$2 (\cot (x) \sin (x)) - \cot (x) = 2 \sin (x) - 1$

Step 1.1.1.3

Rewrite $2 \sin (x) \cot (x)$ in terms of sines and cosines.

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

Step 1.1.1.4

Cancel the common factors.

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

Step 1.1.2

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

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

Step 1.2

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

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

Step 2

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

$x = \frac{π}{6} + 2 π n, \frac{π}{4} + 2 π n, \frac{5 π}{6} + 2 π n, \frac{5 π}{4} + 2 π n$ , for any integer $n$

Step 3