If 2tanx1tan2 x1sqrt3 then x can be equal to check all that

If (2tanx)/(1-tan^2 x)=1/sqrt3, then x can be equal to ________ (check all that apply)

a) x=5pi/12 +npi

b) x=7pi/12 +npi

c) x=11pi/12 +npi

d) x=pi/12 + npi

Solution:

Here;

(2tanx)/(1-tan^2 x)=1/sqrt3

as we know,

tan(2x) = (tanx + tanx ) / (1-tan^2 x)

=> The LHS of the equation is just tan(2x),

=> tan(2x) = 1/sqrt(3)

=> 2x = ( /6) + n ()

=> x = ( /12) + n*( /2)

=> x = /12 + pi/2 + n

=> x = 7 /12 +n

(B)