If `x_1` and `x_2` are two distinct roots of the equation `acosx+bsinx=c ,` then `tan((x_1+x_2)/2)` is equal to (a)`a/b` (b) `b/a` (c) `c/a` (d) `a/c`

Explanation

`acosx+bsinx = c`

`=>(a(1-tan^2(x/2)))/(1+tan^2(x/2))+(b(2tan(x/2)))/(1+tan^2(x/2))= c`

`=>a-atan^2(x/2) +2btan(x/2) = c+ctan^2(x/2)`

`=>(a+c)tan^2(x/2)-2btan(x/2)+(c-a) = 0`

It is a quadratic equation with roots, `tan(x_1/2)` and `tan(x_2/2).`

`:. tan(x_1/2)+tan(x_2/2) = (2b)/(a+c)`

`tan(x_1/2)tan(x_2/2) = (c-a)/(a+c)`

`:. tan((x_1+x_2)/2) = (tan(x_1/2)+tan(x_2/2))/(1-tan(x_1/2)tan(x_2/2))`

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