Trigonometry Examples

$\sin (x) \tan (x) = \sec (x) - \cos (x)$

Step 1

Simplify $\sin (x) \tan (x)$ .

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Raise $\sin (x)$ to the power of $1$ .

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

Step 1.2.3

Raise $\sin (x)$ to the power of $1$ .

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

Step 1.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{\sin (x)}^{1 + 1}}{\cos (x)} = \sec (x) - \cos (x)$

Step 1.2.5

Add $1$ and $1$ .

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

Step 1.3

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

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

Step 1.4

Separate fractions.

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

Step 1.5

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

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

Step 1.6

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

$\sin (x) \tan (x) = \sec (x) - \cos (x)$

Step 2

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

$x \approx 0, 0.1, - 0.3, 0.3, - \frac{2}{5}, \frac{2}{5}, - \frac{1}{2}$

Step 3