Prove that cos 2theta - cos 4theta + cos 6theta - cos 12theta = 4 sin 3theta sin 5theta cos 4theta

What is the slope of a line that is perpendicular to y = 3x + 1

How can you find the conditional probability of a given b as the fraction of b’s outcomes that also belong to a, and interpret the answer in terms of the model? i just need a good explanation

Use the quadratic formula to solve the equation. if necessary, round to the nearest hundredth. x^2 - 20 = x a. 5, 4 b. -5, -4 c. -5, 4 d. 5, -4