Question

If cos x = 3 cos y, then `2 tan  (y - x)/2` is equal to ______.

Options

• `cot  ((y - x)/2)`

• `cot  ((x + y)/4)`

• `cot  ((y - x)/4)`

• `cot  ((x + y)/2)`

Answer 1

If cos x = 3 cos y, then `2 tan  (y - x)/2` is equal to `underlinebb(cot  ((x + y)/2))`.

Explanation:

Given, cos x = 3 cos y

`\implies 3/1 = cosx/cosy`

On applying componendo and dividendo rule, we get

`(3 + 1)/(3 - 1) = (cosx + cosy)/(cosx - cosy)`

`\implies` 2 = `(2cos((x + y)/2)cos((x - y)/2))/(2sin((x + y)/2)sin((y - x)/2))`

`\implies` 2 = `cot((x + y)/2) cot((y - x)/2)`

`\implies 2 tan ((y - x)/2) = cot ((x + y)/2)`