Precalculus Examples

$\csc (θ) (\sin (θ) + \cos (θ))$

Step 1

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

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

Step 2

Apply the distributive property.

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

Step 3

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

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$1 + \frac{1}{\sin (θ)} \cos (θ)$

Step 4

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

$1 + \frac{\cos (θ)}{\sin (θ)}$

Step 5

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

$1 + \cot (θ)$