I need help solving this problem algebraically, but I need to learn step by step!!

Thanks so much

cos 2x=cos x

How do I do it?

2 answers

you should know that
cos 2x = 2cos^2 x - 1

so we have
2cos^2 x - 1 = cosx
2cos^2 x - cosx - 1 = 0
(2cosx + 1)(cosx -1) = 0
cosx = -1/2 or cosx = 1

x = 120° or 240° or x = 0 or 360
in radians
x = 0, 2π/3, 4π/3, 2π
Thanks!
Similar Questions
    1. answers icon 1 answer
  1. A student solves the following equation:Problem: 2(x−3)+3x=19 Step 1: 2x−6+3x=19 Step 2: (2x+3x)−6=19 Step 3: 5x−6=19
    1. answers icon 1 answer
  2. A student solves the following equation:Problem: 2(x−3)+3x=19 Step 1: 2x−6+3x=19 Step 2: (2x+3x)−6=19 Step 3: 5x−6=19
    1. answers icon 1 answer
  3. A student solves the following equation:Problem: 2(x−3)+3x=19 Step 1: 2x−6+3x=19 Step 2: (2x+3x)−6=19 Step 3: 5x−6=19
    1. answers icon 1 answer
more similar questions