If `sinx+cosx=sqrt7/2` where x`in[0,pi/4]` then `tan(x/2)` is equal to

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)`.