Question

If `cosx/(cos(x - 2y))` = λ, then tan (x – y) tan y is eqµal to ______.

Options

• `(1 + λ)/(1 - λ)`

• `(1 - λ)/(1 + λ)`

• `λ/(1 + λ)`

• `λ/(1 - λ)`

Answer 1

If `cosx/(cos(x - 2y))` = λ, then tan (x – y) tan y is eqµal to `underlinebb((1 - λ)/(1 + λ)`.

Explanation:

tan (x – y) tan y

= `(sin(x - y) sin y)/(cos(x - y) cos y) xx 2/2`

= `(cos(x - 2y) - cos (x))/(cos(x - 2y) + cos (x))`

= `(1 - cosx/(cos(x - 2y)))/(1 + cosx/(cos(x - 2y))`   

= `(1 - λ)/(1 + λ)`  ...`[∵ λ = cosx/(cos(x - 2y))]`