​ If tan x =3/2 ,π < x <3π/2, find the value of sinx/2,cosx/2,tanx/2 ​

Question

If tan x = \(\frac{3}{2}\),π < x < \(\frac{3{\pi}}{2}\),find the value of sin\(\frac{x}{2}\),cos\(\frac{x}{2}\),tan\(\frac{x}{2}\)

Answer 1

Given,

tan x = \(\frac{3}{2}\),π< x < \(\frac{3{\pi}}{2}\),   (i. e. x lies in 3^rd quadrant)

Now,

Hence, \(cos\frac{x}{2}=-\frac{1}{10},\)\(sin\frac{x}{2}=-\frac{3}{\sqrt10}\) and
\(tan\frac{x}{2}=-{3}\)