Calculate in surd form, the value of (tan 15°).
-
A.
(2 + sqrt{3}) -
B.
(1 + sqrt{3}) -
C.
(sqrt{3} – 1) -
D.
(2 – sqrt{3})
Correct Answer: Option D
Explanation
(tan 15 = tan (60 – 45))
(tan (x – y) = frac{tan x – tan y}{1 + tan x tan y})
(tan (60 – 45) = frac{tan 60 – tan 45}{1 + tan 60 tan 45})
= (frac{sqrt{3} – 1}{1 + (sqrt{3} times 1)})
= (frac{sqrt{3} – 1}{1 + sqrt{3}})
Rationalizing by multiplying denominator and numerator by (1 – sqrt{3}),
(tan 15 = 2 – sqrt{3})