Question

Find all solutions to the equation. 2cos^(2)x-cosx=0

Answer 1

To find the solutions to the equation 2cos^2(x) - cos(x) = 0, factor the equation and solve each factor separately to obtain the solutions.

Step-by-step explanation:

To find the solutions to the equation 2cos2(x) - cos(x) = 0, we need to factor it and set each factor equal to 0.

First, let's factor out cos(x) from the equation: cos(x)(2cos(x) - 1) = 0.

Now, we have two factors: cos(x) = 0 and 2cos(x) - 1 = 0. Solving each factor, we find the solutions:

• x = π/2 + kπ ,
• x = π/3 + 2kπ
• and x = 0 + 2kπ, where k is an integer.

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