`(sin theta + i cos theta )^4`

Let theta in (pi//4,pi//2), then Statement I (cos theta)^(sin theta ) lt ( cos theta )^(cos theta ) lt ( sin theta )^(cos theta ) Statement II The equation e^(sin theta )-e^(-sin theta )=4 ha a unique solution.

[(1 + cos theta + i sin theta) / (sin theta + i (1 + cos theta))] ^ (4) = cos n theta + i sin n theta

If ((1 + cos theta + i sin theta ) /(i+ sin theta + i cos theta ))= cos ntheta + i sin n theta then n is equal to :

((cos theta+i sin theta)^(4))/((sin theta+i cos theta)^(5)) is equal to.

((cos theta-i sin theta)^(4))/((sin theta+i cos theta)^(5)) is equal to

((cos theta+i sin theta)^(4))/(((sin theta+i cos theta))^(5)) is equal to

If A(theta)=[(sin theta, i cos theta),(i cos theta, sin theta)] , then which of the following is not true ?