Trigonometry Examples

$\tan (2 x) \cos (2 x) = \sin (2 x)$

Step 1

Subtract $\sin (2 x)$ from both sides of the equation.

$\tan (2 x) \cos (2 x) - \sin (2 x) = 0$

Step 2

Simplify $\tan (2 x) \cos (2 x) - \sin (2 x)$ .

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Step 2.1

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 2.1.1

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

$\frac{\sin (2 x)}{\cos (2 x)} \cos (2 x) - \sin (2 x) = 0$

Step 2.1.2

Cancel the common factors.

$\sin (2 x) - \sin (2 x) = 0$

Step 2.2

Subtract $\sin (2 x)$ from $\sin (2 x)$ .

$0 = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.