Question

If `x ((2tan30°)/(1+tan^2 30°)) = y((2tan30°)/(1-tan^2 30°))`, then x : y = ______.

Options

• 1 : 1

• 1 : 2

• 2 : 1

• 4 : 1

Answer 1

If `x((2tan30°)/(1+tan^2 30°))=y((2tan30°)/(1-tan^2 30°))`, then x: y = 2 : 1.

Explanation:

`x((2tan30°)/(1+tan^2 30°))=y((2tan30°)/(1-tan^2 30°))`

⇒ `x/y=(1+tan^2 30°)/(1-tan^2 30°)`

⇒ `x/y=(1+(1/sqrt3)^2)/(1-(1/sqrt3)^2)`

⇒ `x/y=(1+1/3)/(1-1/3)`

⇒ `x/y = (4/3)/(2/3)`

⇒ `x/y = (4xx3)/(3xx2)`

⇒ `x/y = 4/2`

⇒ `x/y = 2/1`

∴ x : y = 2 : 1