If `tan theta = (x sin phi)/(1-x cos phi)` and `tan phi =(y sin theta)/(1-y cos theta)` then the value of `x/y` is

Options

A. `(sin phi)/(sin theta)`
B. `(sin theta)/(sin phi)`
C. `(sin theta)/(1 -cos theta)`
D. `(sin phi)/(1 -cos phi)`

Answer

B

Explanation

We have, ` tan theta = (x sin phi)/( 1- x cos phi)`
` Rightarrow (1 - x cos phi)/(x sin phi) = 1/(tan theta)`
` Rightarrow 1/(x sin phi) - cot phi = cot theta`
` Rightarrow 1/(x sin phi) = cot theta + cot phi`
` and tan phi = (y sin theta)/( 1- y cos theta)`
` Rightarrow 1/(y sin theta) - cot theta = cot phi`
` Rightarrow 1/(y sin theta) = cot phi + cot phi`
` Rightarrow 1/(y sin theta) = 1/(x sin phi)`
` x/y = (sin theta)/(sin phi)`