Trigonometry Examples

$\sin (x) (1 + \cot (x)) = \sin (x) + \cos (x)$

Step 1

Start on the left side.

$\sin (x) (1 + \cot (x))$

Step 2

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

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

Step 3

Simplify.

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Step 3.1

Apply the distributive property.

$\sin (x) \cdot 1 + \sin (x) \frac{\cos (x)}{\sin (x)}$

Step 3.2

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

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

Step 3.3

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

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

Step 4

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

$\sin (x) (1 + \cot (x)) = \sin (x) + \cos (x)$ is an identity