Trigonometry Examples

$\sec (x) \cot (x) = \csc (x)$

Step 1

Simplify $\sec (x) \cot (x)$ .

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Step 1.1

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

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Step 1.1.1

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

$\cot (x) \sec (x) = \csc (x)$

Step 1.1.2

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

$\frac{\cos (x)}{\sin (x)} \cdot \frac{1}{\cos (x)} = \csc (x)$

Step 1.1.3

Cancel the common factors.

$\frac{1}{\sin (x)} = \csc (x)$

Step 1.2

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\csc (x) = \csc (x)$

Step 2

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

$x \approx 0.1, \frac{1}{5}, - 0.3, 0.3, - \frac{2}{5}, \frac{2}{5}, - \frac{1}{2}$

Step 3