Evalute the determinants in queations 1 and 2 :
(i) `[{:(costheta,-sintheta),(sintheta,costheta):}|`
(ii) `|{:(x^(2),-x+1,x-1),(,x+1,x+1):}|`

Explanation

(i) `[{:(costheta,-sintheta),(sintheta,costheta):}]=cos^(2)theta-(-0sin^(2)theta)`
`cos^(2)theta+sin^(2)theta=1`
(ii) `|{:(x^(2),-x+1,x-1),(,x+1,x+1):}|`
`(x^(2)-x+1)(x+1)-(x+1)(x-1)`
`=(x+1)(x^(2)-x+1-1)`
`=x^(3)+x^(2)-2x^(2)-2x+2x+2`
`=x^(3)-x^(2)2`