Express the following in `a+i b` form: `((cos2theta-isin2theta)^4(cos4theta+isin4theta)^(-5))/((cos3theta+isin3theta)^(-2)(cos3theta-isin3theta)^(-9))`

Express the following in a + ib form: (i) ((cos theta+ isin theta)/(sin theta + icos theta))^(4) (ii) ((cos 2theta -isin2theta)^(4)(cos4theta +isin4theta)^(-5))/((cos 3theta +isin3theta)^(-2) (cos 3theta -isin 3theta)^(-9)) (iii) ((sinpi//8 +icos pi//8)^(8))/((sinpi//8-icospi//8)^(8))

Prove that (cos^3theta+sin^3 theta)/(cos theta+sin theta)+(cos^3 theta-sin^3 theta)/(cos theta-sin theta)=2

(sin theta)/(cos3theta)+(sin3theta)/(cos9theta)+(sin9theta)/(cos27theta)+(sin27theta)/(cos81theta)=

Prove that (cos^3 theta-sin^3 theta)/(cos theta-sin theta) = 1+cos theta sin theta

If (costheta +isintheta)(cos2theta +isin2theta).....(cosntheta + isinntheta) = 1 then the value of theta is:

If (costheta+isintheta)(cos2theta+isin2theta)…..(cosntheta+isinntheta)=1 , then the value of theta , is

cos2 theta*cos(theta/(2))-cos3 theta*cos((9theta)/2)=sin5 theta*sin((5theta)/(2))

1 + (cos 2 theta + cos 6 theta)/(cos 4 theta) = (sin 3 theta)/(sin theta).

Prove that: sin4 theta=4 sin theta cos^(3)theta-4cos theta sin^(3)theta

(sin theta)/(cos(3theta))+(sin(3theta))/(cos(9theta))+(sin(9theta))/(cos(27theta))+(sin(27theta))/(cos(81theta))=