if `theta in R` then maximum value of `Delta =|{:(1,,1,,1),(1 ,,1+sintheta,,1),(1 ,, 1,,1+cos theta):}|` is

Options

A. `sqrt(3)//2)`
B. `1//2`
C. `1//sqrt(2)`
D. None of these

Answer

B

Explanation

(2) Applying `C_(2) to C_(2)-C_(1) " and " C_(3) to C_(3) -C_(1)` we get
`Delta =|{:(1,,0,,0),(1,,sin0,,0),(1,,0,,cos 0):}|= sin 0 cos 0 = (sin 2 0)//2`
So maximum value of `Delta ` is `//2`