The maximum value of `|(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)|` is `1/2`

Options

A. `1/2`
B. `(sqrt(3))/2`
C. `sqrt(2)`
D. `(2sqrt(3))/4`

Answer

A

Explanation

Since
`Delta=|(1,1,1),(1,1+sintheta,1),(1+costheta,1,1)|`
`=|(0,0,1),(0,sintheta,1),(costheta,0,1)| [ :'C_(1)toC_(1)-C_(3)` and `C_(2)toC_(2)-C_(3)]`
`=1(sintheta.costheta)`
`=1/2.2sin theta cos theta=1/2sin 2theta`
Since the maximum value of `sin 2theta` is 1. So, for maximum valoue of `theta` should be `45^(@)`
`:. Delta=1/2sin 2.45^(@)`
`=1/2sin90^(@)=1/2.1=1/2`