Algebra Examples

$\sin (θ) \tan (θ) \cot (θ) \csc (θ)$

Step 1

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

$\sin (θ) \frac{\sin (θ)}{\cos (θ)} \cot (θ) \csc (θ)$

Step 2

Multiply $\sin (θ) \frac{\sin (θ)}{\cos (θ)}$ .

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Step 2.1

Combine $\sin (θ)$ and $\frac{\sin (θ)}{\cos (θ)}$ .

$\frac{\sin (θ) \sin (θ)}{\cos (θ)} \cot (θ) \csc (θ)$

Step 2.2

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

$\frac{\sin^{1} (θ) \sin (θ)}{\cos (θ)} \cot (θ) \csc (θ)$

Step 2.3

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

$\frac{\sin^{1} (θ) \sin^{1} (θ)}{\cos (θ)} \cot (θ) \csc (θ)$

Step 2.4

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

$\frac{{\sin (θ)}^{1 + 1}}{\cos (θ)} \cot (θ) \csc (θ)$

Step 2.5

Add $1$ and $1$ .

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

Step 3

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

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

Step 4

Combine.

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

Step 5

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

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Step 5.1

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

$\frac{\sin (θ) (\sin (θ) \cos (θ))}{\cos (θ) \sin (θ)} \csc (θ)$

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

$\frac{\sin (θ) (\sin (θ) \cos (θ))}{\sin (θ) \cos (θ)} \csc (θ)$

Step 5.2.2

Cancel the common factor.

$\frac{\sin (θ) (\sin (θ) \cos (θ))}{\sin (θ) \cos (θ)} \csc (θ)$

Step 5.2.3

Rewrite the expression.

$\frac{\sin (θ) \cos (θ)}{\cos (θ)} \csc (θ)$

Step 6

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

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Step 6.1

Cancel the common factor.

$\frac{\sin (θ) \cos (θ)}{\cos (θ)} \csc (θ)$

Step 6.2

Divide $\sin (θ)$ by $1$ .

$\sin (θ) \csc (θ)$

Step 7

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

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Step 7.1

Reorder $\sin (θ)$ and $\csc (θ)$ .

$\csc (θ) \sin (θ)$

Step 7.2

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

$\frac{1}{\sin (θ)} \sin (θ)$

Step 7.3

Cancel the common factors.

$1$