If z satisfies `z-1/z=2 i sin 5^@` and `z^6+1/z^6=2 i sin theta` then `[|cot theta|]` is equal to (where [ . ] denotes the greater integer function)

lim_(z to 0) [{ max ( sin^(-1) x+ cos^(-1) x)^(2),min (x^(2) + 4x + 7))} . (sin^(-1)z)/z] is equal to ( where [.] denotes greatest integer function )

lim_(z to 0) [{ max ( sin^(-1) x+ cos^(-1) x)^(2),min (x^(2) + 4x + 7))} . (sin^(-1)z)/z] is equal to ( where [.] denotes greatest integer function )

If z = sin theta -i cos theta then for any integer n,

If z = 1 - cos theta + i sin theta , then |z| =

If z=sin theta-i cos theta then for any integer n

If z=r(cos theta +i sin theta ), then the value of (z/ bar z + bar z /z)

If pi < theta < 2pi and z=1+cos theta + i sin theta , then write the value of |z|