Trigonometry Examples

$\frac{\sin (t)}{\tan (t)} + \frac{\cos (t)}{\cot (t)} = \sin (t) + \cos (t)$

Step 1

Start on the left side.

$\frac{\sin (t)}{\tan (t)} + \frac{\cos (t)}{\cot (t)}$

Step 2

Convert to sines and cosines.

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Step 2.1

Write $\tan (t)$ in sines and cosines using the quotient identity.

$\frac{\sin (t)}{\frac{\sin (t)}{\cos (t)}} + \frac{\cos (t)}{\cot (t)}$

Step 2.2

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

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

Step 3

Simplify each term.

$\cos (t) + \sin (t)$

Step 4

Rewrite $\cos (t) + \sin (t)$ as $\sin (t) + \cos (t)$ .

$\sin (t) + \cos (t)$

Step 5

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

$\frac{\sin (t)}{\tan (t)} + \frac{\cos (t)}{\cot (t)} = \sin (t) + \cos (t)$ is an identity