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Let d in R, and A= [{:(-2, " "4+d,("...

Let `d in R`, and
`A= [{:(-2, " "4+d,("sin"theta)-2),(1, ("sin"theta)+2," "d),(5,(2"sin"theta)-d,(-"sin"theta) + 2 +2d):}], theta in [theta, 2 pi].` If the minimum value of det(A) is 8, then a value of d is

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Let d in R, and A[{:(,-2,4+d,(sin theta-2)),(,1,(sin theta)+2,d),(,5,(2sin theta)d,(-sin theta)+2+2d):}]=theta in [0,2pi] If the minimum value of det(A) is B. Then the value of d is:

Let d in R , " and " A = [{:(-2, 4+d, (sin theta) - 2),(2, sintheta+4, 2d),(5, 2sintheta-d, (-sintheta) +2+2d):}] . If the minimum value of det(A) is 16 for all theta in [ 0, 2pi ] , then a value of d is ,

int (d theta)/((sin theta - 2 cos theta)(2 sin theta + cos theta))

int (d theta)/((sin theta - 2 cos theta)(2 sin theta + cos theta))

int_ (0) ^ (pi / 2) ((theta) / (sin theta)) ^ (2) d theta =

int_ (0) ^ ((pi) / (2)) (sin2 theta) / (sin ^ (4) theta + cos (4) theta) d theta

int(d theta)/((sin theta-2cos theta)(2sin theta+cos theta))=

(sin 2 theta)/(sin theta)-(cos 2 theta)/(cos theta)= A) sec theta B) tan theta C)1 D)2

int(d theta)/(sin theta+sin2 theta)