यदि `a=(sqrt(3))/2` है। तो `sqrt(1.a)+sqrt(1-a)` का मान ज्ञात करें।

Options

A. `sqrt(3)`
B. `(sqrt(3))/2`
C. `2+sqrt(3)`
D. `2-sqrt(3)`

Answer

A

Explanation

`a=(sqrt(3))/2impliesa+1=(sqrt(3))/2+1`
`implies(sqrt(3)+2)/2`
`implies(4+2sqrt(3))/4=((sqrt(3)+1)^(2))/4`
`a+1=((sqrt(3)+1)^(2))/4`
`implies sqrt(a+1)=sqrt(((sqrt(3)+1)^(2))/4)`
`sqrt(1+a)=(sqrt(3)+1)/2`
Similarly `sqrt(1-a)=(sqrt(3)-1)/2`
Put values:
`(sqrt(3)+1)/2+(sqrt(3)-1)/2implies(sqrt(3)+1+sqrt(3)-1)/2=(2sqrt(3))/2`
`implies sqrt(3)`