Given that cos 30(^o) = sin 60(^o) = (frac{3}{2}) and sin 30(^o) = cos 60(^o) = (frac{1}{2}), evaluate (frac{tan 60^o – q}{1 – tan 30^o})
-
A.
(sqrt{3 – 2}) -
B.
2 – (sqrt{3}) -
C.
(sqrt{3}) -
D.
-2
Correct Answer: Option C
Explanation
Tan 60 = 3; Tan 30 = 1
(frac{tan 60^o – 1}{1 – tan 30^o}) = (frac{sqrt{3 – 1}}{1 – frac{1}{sqrt{3}}}) = (frac{sqrt{3 – 1}}{frac{3 – 1}{sqrt{3}}})
= (frac{sqrt{3 – 1}}{1} times frac{sqrt{3 – 1}}{sqrt{3}})
= (frac{sqrt{3 – 1}}{1} times frac{sqrt{3}}{sqrt{3}})
= (sqrt{3})