Find the value of (cos(60° + 45°)) leaving your answer in surd form.
-
A.
(frac{6 + sqrt{2}}{4}) -
B.
(frac{3 + sqrt{6}}{4}) -
C.
(frac{sqrt{2} – sqrt{6}}{4}) -
D.
(frac{3 – sqrt{6}}{4})
Correct Answer: Option C
Explanation
(cos (x + y) = cos x cos y – sin x sin y )
(cos (60 + 45) = cos 60 cos 45 – sin 60 sin 45)
= (frac{1}{2} times frac{sqrt{2}}{2} – frac{sqrt{3}}{2} times frac{sqrt{2}}{2})
= (frac{sqrt{2} – sqrt{6}}{4})