Trigonometry Examples

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

Step 1

Rewrite $\csc (t)$ in terms of sines and cosines.

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

Step 2

Apply the distributive property.

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

Step 3

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

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Combine $\frac{1}{\sin (t)}$ and $\cos (t)$ .

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

Step 5

Convert from $\frac{\cos (t)}{\sin (t)}$ to $\cot (t)$ .

$1 + \cot (t)$