Trigonometry Examples

$\csc (x) \tan (x) \sec (x)$

Step 1

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

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Step 1.1

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

$\tan (x) \csc (x) \sec (x)$

Step 1.2

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

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

Step 1.3

Cancel the common factors.

$\frac{1}{\cos (x)} \sec (x)$

Step 2

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\sec (x) \sec (x)$

Step 3

Multiply $\sec (x) \sec (x)$ .

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Step 3.1

Raise $\sec (x)$ to the power of $1$ .

$\sec^{1} (x) \sec (x)$

Step 3.2

Raise $\sec (x)$ to the power of $1$ .

$\sec^{1} (x) \sec^{1} (x)$

Step 3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\sec (x)}^{1 + 1}$

Step 3.4

Add $1$ and $1$ .

$\sec^{2} (x)$