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Evaluate the following determinants: |x-...

Evaluate the following determinants: `|x-7x5x+1|` (ii) `|costheta-sinthetasinthetacostheta|` `|cos15^0sin15^0sin75^0cos75^0|` (iv) `|a+i b c+i d-c+i d a-i b|`

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(i)`|(x,-7),(x,5x+1)|`
Then
`=x(5x+1)+7x`
`=5x^2+12x`
`=x(5x+12)`
(ii)`|(costheta,-sintheta),(sintheta,costheta)|`
Then
`=cos theta cos theta+sin theta sin theta`
...
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