Trigonometry Examples

$\sin^{2} (x) \sec (x) \csc (x)$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Combine.

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

Step 5

Cancel the common factor of $\sin^{2} (x)$ and $\sin (x)$ .

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Step 5.1

Factor $\sin (x)$ out of $\sin^{2} (x) \cdot 1$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Multiply $\sin (x)$ by $1$ .

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

Step 7

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$\tan (x)$