Verify the Pythagorean Identity.

Question

1+cot^2 θ=csc^2 θ

Answer 1

To verify the Pythagorean identity, we start with the given equation:

1 + cot^2 θ = csc^2 θ

Using trigonometric identities, we know that cot^2 θ = 1 + csc^2 θ.

Plugging this in, we get:

1 + 1 + csc^2 θ = csc^2 θ

Simplifying, we get:

2 + csc^2 θ = csc^2 θ

Subtracting csc^2 θ from both sides, we get:

2 = 0

This equation is not true, so the given identity 1 + cot^2 θ ≠ csc^2 θ and is not a valid Pythagorean identity.