Algebra Examples

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

Step 1

Start on the left side.

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

Step 2

Write $\tan (x)$ in sines and cosines using the quotient identity.

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

Step 3

Simplify.

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Step 3.1

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

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

Step 3.2

Reduce the expression by cancelling the common factors.

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Step 3.2.1

Reduce the expression $\frac{\cos (x) \sin (x)}{\cos (x)}$ by cancelling the common factors.

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

$\frac{\frac{\sin (x)}{1}}{\sin (x)}$

Step 3.2.2

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

$\frac{\sin (x)}{\sin (x)}$

Step 3.3

Cancel the common factor of $\sin (x)$ .

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Step 3.3.1

Cancel the common factor.

$\frac{\sin (x)}{\sin (x)}$

Step 3.3.2

Rewrite the expression.

$1$

Step 4

Because the two sides have been shown to be equivalent, the equation is an identity.

$\frac{\cos (x) \tan (x)}{\sin (x)} = 1$ is an identity