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).
Verify the Pythagorean Identity.
1+cot^2 0=csc^2 0
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