Given that sin 60o = (frac{sqrt{3}}{2}) and cos 60o = (frac{1}{2}), evaluate (frac{1 – sin 60^o}{1 + cos 60^o})
-
A.
(frac{2 + sqrt{3}}{3}) -
B.
(frac{1 – sqrt{3}}{3}) -
C.
(frac{1 + sqrt{3}}{3}) -
D.
(frac{2 – sqrt{3}}{3})
Correct Answer: Option D
Explanation
Sin 60 = (frac{sqrt{3}}{2}); cos 60o = (frac{1}{2})
= (frac{1 – sin 60}{1 + cos 60} = frac{1 – frac{sqrt{3}}{2}}{1 + frac{1}{2}})
= (frac{2 – sqrt{3}}{3}{2}div frac{2 + 1}{2})
= (frac{2 – sqrt{3}}{2} times frac{2}{3})
= (frac{2 – sqrt{3}}{3})