1.

Find the maximum value of `|[1, 1, 1],[ 1, 1+sintheta,1],[ 1, 1, 1+costheta]|`

Answer» `D = |[1,1,1],[1,1+sintheta,1],[1,1,1+costheta]|`
Applying `R_2->R_2-R_1` and `R_3->R_3-R_1`

`= |[1,1,1],[0,sintheta,0],[0,0,costheta]|`
`=[1(sinthetacostheta-0)-0+0] `
`=sinthetacostheta`
As `sinxcosx = 1/2sin2x`
`:. D=1/2sin2theta`
We know maximum value of `sin2theta` will be `1`.
So, maximum value of `D` will be ` = 1/2**1 = 1/2`.


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