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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]| = [x(5x+1)+7x] = x(5x+1+7)= x(5x+8)`

(ii)`|[cos theta,-sintheta],[sintheta,cos theta]| = (cos^2theta+sin^2theta) = 1`

(iii) `|[cos15^@,sin15^@],[sin75^@,cos75^@]|`
`= cos15^@cos75^@-sin15^@sin75^@`
`=cos(15^@+75^@) = cos90^@ = 0`
...
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