Prove the identity. 6(tan(x) cot(x)) tan²(x) - cot²(x) Factor the denominator and then simplify. = = 6(tan(x) cot(x)) tan²(x) - cot²(x) (tan(x) + cot(x)) = II 3 sin(2x) = Use the Reciprocal Identities and simplify the compound fraction. 6(tan(x) — cot(x)) tan(x) + cot(x) cos(x) sin(x) cos(x) sin(x) + sin²(x) + cos²(x) Use a Pythagorean Identity and a Double-Angle Formula to simplify. 1

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