Precalculus Examples

$\sec (θ) \sin (θ) \cot (θ) \csc (θ)$

Step 1

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

$\frac{1}{\cos (θ)} \sin (θ) \cot (θ) \csc (θ)$

Step 2

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

$\frac{\sin (θ)}{\cos (θ)} \cot (θ) \csc (θ)$

Step 3

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

$\frac{\sin (θ)}{\cos (θ)} \cdot \frac{\cos (θ)}{\sin (θ)} \csc (θ)$

Step 4

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

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Step 4.1

Cancel the common factor.

$\frac{\sin (θ)}{\cos (θ)} \cdot \frac{\cos (θ)}{\sin (θ)} \csc (θ)$

Step 4.2

Rewrite the expression.

$\frac{1}{\cos (θ)} \cos (θ) \csc (θ)$

Step 5

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

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Step 5.1

Cancel the common factor.

$\frac{1}{\cos (θ)} \cos (θ) \csc (θ)$

Step 5.2

Rewrite the expression.

$1 \csc (θ)$

Step 6

Multiply $\csc (θ)$ by $1$ .

$\csc (θ)$

Step 7

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

$\frac{1}{\sin (θ)}$

Step 8

Convert from $\frac{1}{\sin (θ)}$ to $\csc (θ)$ .

$\csc (θ)$