Trigonometry Examples

$\sin (x) \cos (x) \tan (x) \cot (x) \sec (x) \csc (x)$

Step 1

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

$\sin (x) \cos (x) \frac{\sin (x)}{\cos (x)} \cot (x) \sec (x) \csc (x)$

Step 2

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

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Step 2.1

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

$\cos (x) \sin (x) \frac{\sin (x)}{\cos (x)} \cot (x) \sec (x) \csc (x)$

Step 2.2

Cancel the common factor.

$\cos (x) \sin (x) \frac{\sin (x)}{\cos (x)} \cot (x) \sec (x) \csc (x)$

Step 2.3

Rewrite the expression.

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

Step 3

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

$\sin^{1} (x) \sin (x) \cot (x) \sec (x) \csc (x)$

Step 4

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

$\sin^{1} (x) \sin^{1} (x) \cot (x) \sec (x) \csc (x)$

Step 5

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

${\sin (x)}^{1 + 1} \cot (x) \sec (x) \csc (x)$

Step 6

Add $1$ and $1$ .

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

Step 7

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

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

Step 8

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

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Step 8.1

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

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

Step 8.2

Cancel the common factor.

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

Step 8.3

Rewrite the expression.

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

Step 9

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

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

Step 10

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

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Step 10.1

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

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

Step 10.2

Cancel the common factor.

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

Step 10.3

Rewrite the expression.

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

Step 11

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

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Step 11.1

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

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

Step 11.2

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

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

Step 11.3

Cancel the common factors.

$1$