Question

what is ( 4cos^{2}(165^{circ}) - 2 ) expressed as a single trigonometric function?
( 4cos(330^{circ}) )
( 2cos(330^{circ}) )
( 4cos(82.5^{circ}) )
( 2cos(82.5^{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

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Answer:

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