The value of 2tan 30°/(1 + tan^2 30°) is: (a) 1/2 (b) 1/√3 (c) √3/2 (d) √3

Question

The value of \(\frac{2tan30°}{1+tan^230°}\) is: 

(a) \(\frac{1}{2}\)

(b) \(\frac{1}{\sqrt{3}}\)

(c) \(\frac{\sqrt3}{2}\)

(d) √3

Answer 1

(d) √3

We know that sin 2A = \(\frac{2tanA}{1+tan^2A}\)

\(\frac{2tan30°}{1+tan^230°}\) = sin(2 x 30°) = sin 60° = \(\frac{\sqrt{3}}{2}\)

= tan 2A 

= tan 60° 

= √3