Simplify tan(2)(x)-tan(2)xsin(2)x

$\tan (2) (x) - \tan (2) x \sin (2) x$

Step 1

Simplify each term.

Rewrite $\tan (2)$ in terms of sines and cosines.

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

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

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{\sin (2) x}{\cos (2)} - \tan (2) (x \cdot x) \sin (2)$

Multiply $x$ by $x$ .

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

Rewrite $\tan (2)$ in terms of sines and cosines.

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

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

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

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

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

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

Raise $\sin (2)$ to the power of $1$ .

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

Raise $\sin (2)$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Step 2

Simplify each term.

Separate fractions.

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

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

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

Divide $x$ by $1$ .

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

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

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

Separate fractions.

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

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

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

Divide $x^{2} (\sin (2))$ by $1$ .

$x \tan (2) - x^{2} \sin (2) \tan (2)$