Question

Find the value of `cos(x/2)`, if tan x = `5/12` and x lies in third quadrant.

Options

• `5/sqrt(13)`

• `5/sqrt(26)`

• `5/13`

• `sqrt(1/26)`

Answer 1

`bb(sqrt(1/26))`

Explanation:

Given, tanx = `5/12` and x lies in III quadrant.

∴ sinx = `(-5)/13` and cosx = `(-12)/13`

Now, cosx = `2cos^2  x/2 - 1`

`\implies cos^2  x/2 = 1/2(cosx + 1)`

= `1/2((-12)/13 + 1)`

= `1/2(1/13)`

= `1/26`

∴ `cos  x/2 = sqrt(1/26)`