Determine if True (cos(x)tan(x))/(sin(x))=1

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

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.

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

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

Reduce the expression by cancelling the common factors.

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factor.

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

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