Evaluate 1+cot(theta)^2=csc(theta)^2

$1 + \cot^{2} (θ) = \csc^{2} (θ)$

Step 1

Apply pythagorean identity.

$\csc^{2} (θ) = \csc^{2} (θ)$

Step 2

For the two functions to be equal, the arguments of each must be equal.

$θ = θ$

Step 3

Move all terms containing $θ$ to the left side of the equation.

Subtract $θ$ from both sides of the equation.

$θ - θ = 0$

Subtract $θ$ from $θ$ .

$0 = 0$

Step 4

Since $0 = 0$ , the equation will always be true.

Always true

Step 5

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$