To solve the equation:

\[
\cos 2x - \cos x + 1 = 0
\]

we'll use a trigonometric identity for \(\cos 2x\) and simplify.

### Step 1: Substitute the Double Angle Identity
The double angle identity for cosine is:
\[
\cos 2x = 2 \cos^2 x - 1
\]

Substitute this into the equation:

\[
2 \cos^

Learn how to solve the trigonometric equation cos 2x - cos x + 1 = 0 with a detailed step-by-step solution. This problem involves the double angle identity for cosine and is suitable for high school students studying trigonometry in Grades 10-12.

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