Trigonometry Examples

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

Step 1

Simplify $2 \tan^{2} (x) + \sin^{2} (x)$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

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

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

Step 1.1.2

Apply the product rule to $\frac{\sin (x)}{\cos (x)}$ .

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

Step 1.1.3

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

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

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Multiply by $1$ .

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

Step 1.2.2

Multiply by $1$ .

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

Step 1.2.3

Separate fractions.

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

Step 1.2.4

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

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

Step 1.2.5

Multiply $2$ by $1$ .

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

Step 1.2.6

Divide $2$ by $1$ .

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

Step 2

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

$x \approx 0.5440881 + π n, 2.59750454 + π n$ , for any integer $n$

Step 3