(a) Derive the trigonometric addition formulas for cos(α+β) and sin(α+β) using the Euler's formula. Start from e i(α+β) = e iαe iβ, expand all exponential functions using the Euler's formula and equate the real and imaginary parts from the left and right-hand sides of the equation.

5, 6, 10 question: a. determine whether the side lengths form a triangle. (explain your reasoning) b. if it is a triangle, determine whether it is a right, acute, or obtuse triangle. (show your work)

Polynomials plz quick 1: subtract and simplify (–y^2 – 4y – 8) – (–4y^2 – 6y + 3)

Walgreens sells both kleenex and nyquil. in a random sample of 5000 purchases, it was found that 1200 contained kleenex and 540 contained nyquil. these are not independent because sick people are more likely to buy both and healthy people more likely to buy neither. in looking into that, it was found that 360 purchases contained both. a. make a two-way table to display this information. fill in the table with the missing entries, and be sure your table has row and column totals. b. if we randomly select a purchase that contained kleenex, what is the probability it also contained nyquil? c. what percent of all purchases didn’t contain either product?