Question

If `sqrt((1 + cos A)/(1 - cos A)) = x/y`, then the value of tan A is ______.

Options

• `(x^2 + y^2)/(x^2 - y^2)`

• `(2xy)/(x^2 + y^2)`

• `(2xy)/(x^2 - y^2)`

• `(2xy)/(y^2 - x^2)`

Answer 1

If `sqrt((1 + cos A)/(1 - cos A)) = x/y`, then the value of tan A is `underlinebb((2xy)/(x^2 - y^2)`.

Explanation:

`sqrt((1 + cos A)/(1 - cos A))`

= `sqrt((2 cos^2  A/2)/(2 sin^2  A/2))`

= `x/y`

`\implies tan  A/2 = y/x` 

Now, tan A = `(2 tan  A/2)/(1 - tan^2  A/2)`

= `(2xy)/(x^2 - y^2)`