Find tan x2 given that tan x 3 and x terminates in pi Solut

Find tan x/2, given that tan x = 3 and x terminates in pi

Solution

tan x=3 and x is in third quadrant.

Here opposite=3 and adjacent=1

Hypotenuse= sqrt(3²+1²) = sqrt10

In third quadrant both sine and cosine are negative.

Cos x= adjacent /hypotenuse =-1/sqrt10

Sin x= opposite/hypotenuse=-3/sqrt10

Tan(x/2)= (1-cos x)/sin x = (1 - (-1/sqrt10))/-3/sqrt10

= (sqrt10 +1)/-3

Correct option is A