Find, in surd form, the value of (cos 165).

Find, in surd form, the value of (cos 165).

Correct Answer: Option D

Explanation

(cos 165 = -cos (180 – 165) = -cos 15)

(cos 15 = cos (45 – 30))

(cos (x – y) = cos x cos y + sin x sin y)

(cos (45 – 30) = cos 45 cos 30 + sin 45 sin 30)

= ((frac{sqrt{2}}{2})(frac{sqrt{3}}{2}) + (frac{sqrt{2}}{2})(frac{1}{2}))

= (frac{1}{4}(sqrt{6} + sqrt{2}))

(therefore cos 165 = -frac{1}{4}(sqrt{6} + sqrt{2}))