If `sinx+cosx=(sqrt(7))/2,` where `x in 1s t` quadrant, then `tanx/2` is equal to `(3-sqrt(7))/3` (b) `(sqrt(7)-2)/3` (c) `(4-sqrt(7))/4` (d) none of these

Options

A. `(3-sqrt(7))/(3)`
B. `(sqrt(7)-2)/(3)`
C. `(4-sqrt(7))/(4)`
D. none of these.

Answer

B

Explanation

`sin x+cos x=sqrt(7)/(2)`
`rArr(2tan((x)/(2)))/(1+tan^(2)((x)/(2)))+(1-tan^(2)((x)/(2)))/(1+tan^(2)((x)/(2)))=sqrt(7)/(2)`
or `(sqrt(7)+2)tan^(2)((x)/(2))-4tan((x)/(2))+(sqrt(7)-2)=0`
or `tan((x)/(2))=(4+-sqrt(16+4(7-4)))/(2(sqrt(7)+2))=(1)/(sqrt(7)+2))("as "(x)/(2)lt(pi)/(8))`
`=(sqrt(7)-2)/(3)`.