which of the following is a solution of 2cos^2x-cost-1=0 a. 0 degrees b. 150 degrees c. 180 degrees d. 210 degrees

{0, 150} degrees

Step-by-step explanation:

Given 2cos^2x-cost-1=0, let's simplify this problem by temporarily replacing cos x with y:

2y^2 - y - 1 = 0

This can be solved by factoring: (2y + 1) (y - 1) = 0. From this we get two solutions: y = - 1/2 and y = 1.

Remembering that we let y = cos x, we now solve:

cos x = - 1/2 and cos x = 1.

Note that cos x = 1 when x = 0 and the "adjacent side" coincides with the hypotenuse.

cos x = - 1/2 when the hypotenuse is 2 and the "adjacent side" is - 1. This has two solutions between 0 and 360 degrees: 150 degrees and 270 degrees.

Four answer choices are given. Both (a) (0 degrees) and (b) (150 degrees) satisfy the original equation. Thus, the solution set is {0, 150} (degrees).