4(tan(x) − cot(x)) tan2(x) − cot2(x) = 2 sin(2x) Factor the denominator and then simplify. 4(tan(x) − cot(x)) tan2(x) − cot2(x) = 4(tan(x) − cot(x)) (tan(x) + cot(x)) = tan(x) + cot(x) Use the Reciprocal Identities and simplify the compound fraction. = sin(x) cos(x) + cos(x) sin(x) = sin2(x) + cos2(x) Use a Pythagorean Identity and a Double-Angle Formula to simplify. = 1 =