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Aishwarya Kannan
Asked: 2022-11-09T06:44:44+05:30 In:

If `x_(1)` and `x_(2)` are two distind roots of the equation `a cos x+b sinx=c`, then `tan”” (x_(1)+x_(2))/(2)` is equal to
A. `(a)/(b)`
B. `(b)/(a)`
C. `(c)/(a)`
D. `(a)/(c)`

If `x_(1)` and `x_(2)` are two distind roots of the equation `a cos x+b sinx=c`, then `tan”” (x_(1)+x_(2))/(2)` is equal to
A. `(a)/(b)`
B. `(b)/(a)`
C. `(c)/(a)`
D. `(a)/(c)`
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  1. Correct Answer – B
    `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)`

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