Evaluate (cos 75°), leaving the answer in surd form.
-
A.
(frac{sqrt{2}}{2}(sqrt{3} + 1)) -
B.
(frac{sqrt{2}}{4}(sqrt{3} – 1)) -
C.
(frac{sqrt{2}}{4}(sqrt{3} + 1)) -
D.
(frac{sqrt{2}}{2}(sqrt{3} – 1))
Correct Answer: Option B
Explanation
(cos(a + b) = cos acos b – sin asin b)
(cos75° = cos(30 + 45) = (cos30)(cos45) – (sin30)(sin45))
= ((frac{sqrt{3}}{2} times frac{sqrt{2}}{2}) – (frac{1}{2} times frac{sqrt{2}}{2}))
= (frac{sqrt{6} – sqrt{2}}{4})
= (frac{sqrt{2}(sqrt{3} – 1)}{4})