Question

Verify the Pythagorean Identity.

1+cot^2 0=csc^2 0

Answer 1

[AI-generated answer — Bot GPT 3.5]

To verify the Pythagorean identity, we need to show that the following equation holds true:

1 + cot^2(θ) = csc^2(θ)

First, we know that cot(θ) = 1/tan(θ) and csc(θ) = 1/sin(θ).

Substitute cot(θ) and csc(θ) into the equation:

1 + (1/tan(θ))^2 = (1/sin(θ))^2

1 + (1/sin(θ))^2 = (1/sin(θ))^2

1 + 1/sin^2(θ) = 1/sin^2(θ)

Multiply both sides by sin^2(θ):

sin^2(θ) + 1 = 1

sin^2(θ) = 1

This verifies the Pythagorean identity: 1 + cot^2(θ) = csc^2(θ).