Trigonometry Examples

$\sin (x) \cdot \cos (x) \cdot \sec (x) \cdot \csc (x)$

Step 1

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

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

Step 2

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

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Step 2.1

Factor $\cos (x)$ out of $\sin (x) \cos (x)$ .

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

$\sin (x) \cdot \csc (x)$

Step 3

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 3.1

Reorder $\sin (x)$ and $\csc (x)$ .

$\csc (x) \cdot \sin (x)$

Step 3.2

Rewrite $\sin (x) \cdot \csc (x)$ in terms of sines and cosines.

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

Step 3.3

Cancel the common factors.

$1$

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