Algebra Examples

$\csc (θ) \cot^{2} (θ) + \csc (θ)$

Step 1

Reorder $\csc (θ) \cot^{2} (θ)$ and $\csc (θ)$ .

$\csc (θ) + \csc (θ) \cot^{2} (θ)$

Step 2

Multiply by $1$ .

$\csc (θ) \cdot 1 + \csc (θ) \cot^{2} (θ)$

Step 3

Simplify with factoring out.

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Step 3.1

Factor $\csc (θ)$ out of $\csc (θ) \cot^{2} (θ)$ .

$\csc (θ) \cdot 1 + \csc (θ) (\cot^{2} (θ))$

Step 3.2

Factor $\csc (θ)$ out of $\csc (θ) \cdot 1 + \csc (θ) (\cot^{2} (θ))$ .

$\csc (θ) \cdot (1 + \cot^{2} (θ))$

Step 4

Apply pythagorean identity.

$\csc (θ) \cdot \csc^{2} (θ)$

Step 5

Multiply $\csc (θ)$ by $\csc^{2} (θ)$ by adding the exponents.

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Step 5.1

Multiply $\csc (θ)$ by $\csc^{2} (θ)$ .

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Step 5.1.1

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

$\csc^{1} (θ) \cdot \csc^{2} (θ)$

Step 5.1.2

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

${\csc (θ)}^{1 + 2}$

Step 5.2

Add $1$ and $2$ .

$\csc^{3} (θ)$