Question

If tan x = `3/4, π < x < (3π)/2`, then the value of `cos  x/2` is ______.

Options

• `-1/sqrt(10)`

• `3/sqrt(10)`

• `1/sqrt(10)`

• `-3/sqrt(10)`

Answer 1

If tan x = `3/4, π < x < (3π)/2`, then the value of `cos  x/2` is `underlinebb(-1/sqrt(10))`.

Explanation:

Given, tan x = `3/4, π < x < (3π)/2`

`\implies` cos x = `-4/5`

∵ 1 + cos x = `2 cos^2 (x/2)`

∴ `1 - 4/5 = 2cos^2(x/2)`

`\implies 1/5 = 2 cos^2(x/2)`

`\implies cos^2(x/2) = 1/10`

`\implies cos(x/2) = ± 1/sqrt(10)`

`\implies cos(x/2) = -1/sqrt(10)`  ...`[∵ π/2 < x/2 < (3π)/4]`