`((cos2 theta+i sin2 theta)^(3)(cos3 theta-i sin3 theta)^(5))/((cos3 theta+i sin3 theta)^(2)(cos4 theta+i sin4 theta)^(3))=`

Express the following in a+ib form: ((cos2 theta-i sin2 theta)^(4)(cos4 theta+i sin4 theta)^(-5))/((cos3 theta+i sin3 theta)^(-2)(cos3 theta-i sin3 theta)^(-9))

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

((cos3 theta+i sin3 theta)^(5)(cos theta-i sin theta)^(3))/((cos5 theta+i sin5 theta)^(7)(cos2 theta-i sin2 theta)^(5))

(cos theta + i sin theta)^3 xx (cos theta-i sin theta)^4=

The number of values of theta in (0, pi] , such that (cos theta + i sin theta) (cos 3 theta + i sin 3 theta) (cos 5 theta + i sin 5 theta) (cos 7 theta + i sin 7 theta) (cos 9 theta + i sin 9 theta) = -1 is

((cos theta + i sin theta) / (sin theta + i cos theta)) ^ (4) = cos8 theta + i sin8 theta

Prove each of the following identities : (cos^(3) theta + sin^(3) theta)/(cos theta + sin theta ) + (cos^(3) theta - sin^(3) theta)/(cos theta - sin theta ) = 2

In the form of A+iBz=(cos2 theta+i sin2 theta)^(-5)(cos3 theta-i sin3 theta)^(6)(sin theta-i cos theta)^(3) is

(3sin theta-sin3 theta)/(3cos theta+cos3 theta)=

(sin3 theta-sin theta)/(cos theta-cos3 theta)=cot2 theta