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

1 Answer
Psykolord1989 .
Apr 29, 2016

(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

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