Trigonometry Examples

$2 \sin (x) \cos (x) \sec (x) \csc (x)$

Step 1

Apply the sine double-angle identity.

$\sin (2 x) \sec (x) \csc (x)$

Step 2

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

$\sin (2 x) \frac{1}{\cos (x)} \csc (x)$

Step 3

Combine $\sin (2 x)$ and $\frac{1}{\cos (x)}$ .

$\frac{\sin (2 x)}{\cos (x)} \csc (x)$

Step 4

Apply the sine double-angle identity.

$\frac{2 \sin (x) \cos (x)}{\cos (x)} \csc (x)$

Step 5

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

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Step 5.1

Cancel the common factor.

$\frac{2 \sin (x) \cos (x)}{\cos (x)} \csc (x)$

Step 5.2

Divide $2 \sin (x)$ by $1$ .

$2 \sin (x) \csc (x)$

Step 6

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

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Step 6.1

Add parentheses.

$2 (\sin (x) \csc (x))$

Step 6.2

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

$2 (\csc (x) \sin (x))$

Step 6.3

Rewrite $2 \sin (x) \csc (x)$ in terms of sines and cosines.

$2 (\frac{1}{\sin (x)} \sin (x))$

Step 6.4

Cancel the common factors.

$2 \cdot 1$

Step 7

Multiply $2$ by $1$ .

$2$