Trigonometry Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

$\frac{\sin (x)}{\cos (x)} \cdot \frac{1}{\cos (x)} \sin (x) = \tan^{2} (x)$

Step 1.3

Multiply $\frac{\sin (x)}{\cos (x)} \cdot \frac{1}{\cos (x)}$ .

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Step 1.3.1

Multiply $\frac{\sin (x)}{\cos (x)}$ by $\frac{1}{\cos (x)}$ .

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

Step 1.3.2

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

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

Step 1.3.3

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

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

Step 1.3.4

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

$\frac{\sin (x)}{{\cos (x)}^{1 + 1}} \sin (x) = \tan^{2} (x)$

Step 1.3.5

Add $1$ and $1$ .

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

Step 1.4

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

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Step 1.4.1

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

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

Step 1.4.2

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

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

Step 1.4.3

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

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

Step 1.4.4

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

$\frac{{\sin (x)}^{1 + 1}}{\cos^{2} (x)} = \tan^{2} (x)$

Step 1.4.5

Add $1$ and $1$ .

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

Step 1.5

Convert from $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ to $\tan^{2} (x)$ .

$\tan^{2} (x) = \tan^{2} (x)$

Step 2

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

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

Step 3