Simplify : `((1+ cos theta - isin theta)/(1+cos theta + i sin theta))^5 `

Simplify ((1 + cos 2 theta + i sin 2 theta)/(1 + cos 2 theta - i sin 2 theta))^(30)

((cos theta + i sin theta)^(6))/((cos theta - isin theta)^(5)) = ________

Prove each of the following identities : (i) (1+ cos theta + sin theta)/(1+ cos theta - sin theta) =(1+ sin theta)/(cos theta) (ii) (sin theta + 1- cos theta)/(cos theta - 1 + sin theta) = (1+ sin theta)/(cos theta)

(1+cos theta+i sin theta)^(10)+(1+cos theta-i sin theta)^(10)=

(1 + sin theta-cos theta) / (1 + sin theta + cos theta)

If (1 + cos theta + isin theta) (1 + cos 2 theta + isin 2theta) = x + iy then y =

((cos theta+isin theta)^4)/((sin theta+icos theta)^5)=?

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

(sin theta)/(1-cos theta)=(1+cos theta)/(sin theta)

(1 + cos theta + sin theta) / (1 + cos theta-sin theta) = (1 + sin theta) / (cos theta)