which expression is equivalent to 2cos²(x/2) - cos(x)?\n0\n1\n1 - 2cos(x)\n1 + 2cos(x)

Explanation:

Step1: Use the half - angle identity

Recall the double - angle formula $\cos(2\alpha)=2\cos^{2}\alpha - 1$. Let $\alpha=\frac{x}{2}$, then $2\cos^{2}(\frac{x}{2})=1 + \cos(x)$.

Step2: Substitute into the given expression

Substitute $2\cos^{2}(\frac{x}{2})=1+\cos(x)$ into $2\cos^{2}(\frac{x}{2})-\cos(x)$. We get $(1 + \cos(x))-\cos(x)$.

Step3: Simplify the expression

$(1+\cos(x))-\cos(x)=1+\cos(x)-\cos(x)=1$.

Answer:

1