Trigonometry Examples

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

Step 1

Simplify $1 + \cot^{2} (- x)$ .

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Step 1.1

Apply pythagorean identity.

$\csc^{2} (- x) = \csc^{2} (x)$

Step 1.2

Since $\csc (- x)$ is an odd function, rewrite $\csc (- x)$ as $- \csc (x)$ .

${(- \csc (x))}^{2} = \csc^{2} (x)$

Step 1.3

Apply the product rule to $- \csc (x)$ .

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

Step 1.4

Raise $- 1$ to the power of $2$ .

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

Step 1.5

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

$\csc^{2} (x) = \csc^{2} (x)$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 0, 0.1, \frac{1}{5}, 0.3, - \frac{2}{5}, \frac{2}{5}, \frac{1}{2}$

Step 3