Question

How do you simplify `(sin^2 theta + cos^2 theta) / tan^2 theta`?

Answer 1

`(sin^2 theta + cos^2 theta)/tan^2 theta = cot^2 theta`

Explanation:

Recall from our trigonometric identities that `sin^2 theta + cos^2 theta = 1`. Then the expression becomes:

`(sin^2 theta + cos^2 theta)/tan^2 theta = 1/(tan^2 theta)`

We also know from the definition of cotangent that `cot theta = 1/tan theta`. Squaring both sides, we obtain `cot^2 theta = (1/tan theta)^2 = 1^2/tan^2 theta = 1/tan^2 theta`