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If theta in R then maximum value of De...

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

A

`sqrt(3)//2`

B

`1//2`

C

`1//sqrt(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
(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`
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