Trigonometry Examples

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

Step 1

Start on the right side.

$\frac{\cos (x)}{\cot^{2} (x)}$

Step 2

Convert to sines and cosines.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Simplify.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2

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

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

Step 4

Rewrite $\frac{\sin^{2} (x)}{\cos (x)}$ as $\sin (x) \tan (x)$ .

$\sin (x) \tan (x)$

Step 5

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

$\sin (x) \tan (x) = \frac{\cos (x)}{\cot^{2} (x)}$ is an identity