Trigonometry Examples

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

Step 1

Start on the left side.

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

Step 2

Apply pythagorean identity.

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

Step 3

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

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

Step 4

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

$\sin (x) \cos (x)$

Step 5

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

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