what is ( 4cos^{2}(165^{circ}) - 2 ) expressed as a single trigonometric function?\n( 4cos(330^{circ}) )\n(…

Answer:

B. (2\cos(330^{\circ}))

Explanation:

Step1: Use double - angle formula

The double - angle formula for cosine is (\cos(2\alpha)=2\cos^{2}\alpha - 1), so (2\cos^{2}\alpha=\cos(2\alpha)+ 1). For the expression (4\cos^{2}(165^{\circ})-2), we can rewrite it as (2(2\cos^{2}(165^{\circ}))-2). Substitute (2\cos^{2}\alpha=\cos(2\alpha)+1) with (\alpha = 165^{\circ}), then (2(2\cos^{2}(165^{\circ}))-2=2(\cos(2\times165^{\circ}) + 1)-2).

Step2: Simplify the expression

[ \begin{align*} 2(\cos(330^{\circ})+1)-2&=2\cos(330^{\circ})+2 - 2\ &=2\cos(330^{\circ}) \end{align*} ]