If `cosx=(2cosy-1)/(2-cosy),` where `x , y in (0,pi)` then `tan(x/2)cot(y/2)` is equal to `sqrt(2)` (b) `sqrt(3)` (c) `1/(sqrt(2))` (d) `1/(sqrt(3))`

Options

A. `sqrt(2)`
B. `sqrt(3)`
C. `(1)/sqrt(2)`
D. `(1)/sqrt(3)`

Answer

B

Explanation

`cos x=(2cos y-1)/(2-cosy)`
`rArr(1-tan^(2)((x)/(2)))/(1+tan^(2)((X)/(2)))=((2(1-tan^(2)y//2))/(1+tan^(2)y//2))/(2-(1-tan^(2)y//2)/(1+tan^(2)y//2))=((1-3tan^(2)((y)/(2)))/(1+3tan^(2)((y)/(2))))`
`rArr tan^(2)((x)/(2))=3tan^(2)((y)/(2))`
or `tan((x)/(2))cot((y)/(2))=sqrt(3)`.