If `x_1a n dx_2` are two distinct roots of the equation `acosx+bsinx=c ,` then tan `(x_(1+x^2))/2` is equal to `a/b` (b) `b/a` (c) `c/a` (d) `a/c`

Options

A. `(a)/(b)`
B. `(b)/(a)`
C. `(c)/(a)`
D. `(a)/(c)`

Answer

B

Explanation

`a cos x+b sin x=c`
`rArr (a(1-tan^(2)(x)/(x)))/(1+tan^(2)(x)/(2))+(2btan((x)/(2)))/(1+tan^(2)((x)/(2)))=c`
`rArr(c+a)tan^(2)((x)/(2))-2btan((x)/(2))+c-a=0`
`rARr tan((x_(1))/(2))+tan ((x^(2))/(2))=(2b)/(c+a)`
and `tan((x_(1))/(2))tan((x_(2))/(2))=(c-a)/(c+a)`
`rArr tan((x_(1)+x_(2))/(2))=((2b)/(c+a))/(1-(c-a)/(c+a))=(2b)/(2a)=(b)/(a)`