Question

If tan x=1/\(\sqrt{3}\), then sin 2x =___________________

(a) 1/\(\sqrt{2}\)

(b) 1/2

(c) \(\sqrt{3}\)/2

(d) 1

I got this question during an online interview.

My doubt is from Trigonometric Functions of Sum and Difference of Two Angles-2 in chapter Trigonometric Functions of Mathematics – Class 11

Answer 1

Correct option is (c) \(\sqrt{3}\)/2

For explanation I would say: We know, sin 2x = (2 tan x) / (1 + tan^2x)

sin 2x=(2*1/\(\sqrt{3}\)) / (1+1/3) = (2*3)/4*\(\sqrt{3}\) = \(\sqrt{3}\)/2.