simplify `((e^(i theta)-e^(-i theta)))/(i(e^(i theta)+e^(-i theta)))` where `e^(itheta)=a+ib`

((1+i tan theta)/(1-i tan theta))^(n)-(1+i tan n theta)/(1-i tan n theta)=

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

z_2/z_1 = (A) e^(itheta) cos theta (B) e^(itheta) cos 2theta (C) e^(-itheta) cos theta (D) e^(2itheta) cos 2theta

If z=re^(i theta), then prove that |e^(iz)|=e^(-r sin theta)

int_(-pi/4) ^(pi/4) (e^theta(thetasintheta))/(e^(2theta)-1)d theta=

x=e^(theta)(theta+(1)/(theta)),y = e^(-theta)(theta-(1)/(theta))

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

"(cos theta+i sin theta)^(6)(cos theta-i sin theta)^(-3)

Show that e^(2mi theta)((i cot theta+1)/(i cot theta-1))^(m)=1

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