Algebra Examples

$1 + 2 \cot^{2} (θ) + \cot^{4} (θ) = {\csc (θ)}^{n}$

Step 1

Replace the $2 \cot^{2} (θ)$ with $2 (\csc^{2} (θ) - 1)$ based on the $\cot^{2} (x) + 1 = \csc^{2} (x)$ identity.

$1 + 2 (\csc^{2} (θ) - 1) + \cot^{4} (θ) = {\csc (θ)}^{n}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the distributive property.

$1 + 2 \csc^{2} (θ) + 2 \cdot - 1 + \cot^{4} (θ) = {\csc (θ)}^{n}$

Step 2.2

Multiply $2$ by $- 1$ .

$1 + 2 \csc^{2} (θ) - 2 + \cot^{4} (θ) = {\csc (θ)}^{n}$

Step 3

Subtract $2$ from $1$ .

$2 \csc^{2} (θ) - 1 + \cot^{4} (θ) = {\csc (θ)}^{n}$

Step 4

Reorder the polynomial.

$\cot^{4} (θ) + 2 \csc^{2} (θ) - 1 = {\csc (θ)}^{n}$