Calculus Examples

$1 + \csc^{2} (x) = \cot^{2} (x)$

Step 1

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

$1 (\cot^{2} (x) + 1) = \cot^{2} (x)$

Step 2

Multiply $\cot^{2} (x) + 1$ by $1$ .

$\cot^{2} (x) + 1 = \cot^{2} (x)$

Step 3

Move all terms containing $\cot (x)$ to the left side of the equation.

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Step 3.1

Subtract $\cot^{2} (x)$ from both sides of the equation.

$\cot^{2} (x) + 1 - \cot^{2} (x) = 0$

Step 3.2

Combine the opposite terms in $\cot^{2} (x) + 1 - \cot^{2} (x)$ .

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Step 3.2.1

Subtract $\cot^{2} (x)$ from $\cot^{2} (x)$ .

$0 + 1 = 0$

Step 3.2.2

Add $0$ and $1$ .

$1 = 0$

Step 4

Since $1 \neq 0$ , there are no solutions.

No solution