Trigonometry Examples

$\frac{\sin (x)}{\cos^{2} (x)} = \sec (x) \tan (x)$

Step 1

Simplify $\frac{\sin (x)}{\cos^{2} (x)}$ .

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Step 1.1

Factor $\cos (x)$ out of $\cos^{2} (x)$ .

$\frac{\sin (x)}{\cos (x) \cos (x)} = \sec (x) \tan (x)$

Step 1.2

Separate fractions.

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

Step 1.3

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

$\frac{1}{\cos (x)} \tan (x) = \sec (x) \tan (x)$

Step 1.4

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\sec (x) \tan (x) = \sec (x) \tan (x)$

Step 2

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

$x \approx 0, - 0.1, 0.1, - \frac{1}{5}, \frac{1}{5}, - 0.3, 0.3$

Step 3