Simplify (frac{tan 80° – tan 20°}{1 + tan 80° tan 20°})
-
A.
(3sqrt{2}) -
B.
(2sqrt{3}) -
C.
(sqrt{3}) -
D.
(sqrt{2})
Correct Answer: Option C
Explanation
(tan (x – y) = frac{tan x – tan y}{1 + tan x tan y})
(implies frac{tan 80 – tan 20}{1 + tan 80 tan 20} = tan (80 – 20) = tan 60°)
(tan 60 = frac{sin 60}{cos 60} = frac{sqrt{3}}{2} ÷ frac{1}{2})
= (sqrt{3})