Trigonometry Examples

$(1 - \cos^{2} (x)) \cot^{2} (x) = \cos^{2} (x)$

Step 1

Start on the left side.

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

Step 2

Apply pythagorean identity.

$\sin^{2} (x) \cot^{2} (x)$

Step 3

Convert to sines and cosines.

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Step 3.1

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

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

Step 3.2

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

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

Step 4

Cancel the common factor of ${\sin (x)}^{2}$ .

$\cos^{2} (x)$

Step 5

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

$(1 - \cos^{2} (x)) \cot^{2} (x) = \cos^{2} (x)$ is an identity