If `theta` is an acute angle and `sin((theta)/(2))=sqrt((x-1)/(2x))` ,then `tan theta` is equal to

Answer

`tantheta=sqrt(x^(2)-1)`

Explanation

`cos^(2)""(theta)/(2)=1-sin^(2)""(theta)/(2)=1-(x-1)/(2x)=(x+1)/(2x)`
`rArr tan(theta)/(2)=sqrt((X-1)/(2x))+sqrt((x+1)/(2x))=sqrt((x-1)/(x+1))`
`rArr tan theta=(2tan (theta//2))/(1-tan^(2)(theta//2))`
`rArr tan theta=(2tan (theta//2))/(1-tan^(2)(theta//2))`
`=(2sqrt((x-1)/(x+1)))/(1-(x-1)/(x+1))=sqrt(x-1)sqrt(x+1)=sqrt(x^(2)-1)`