Solve `(cos theta +isin theta)^6.(cos theta - isin theta)^-3`

Solve : cos p theta = sin q theta.

Solve 3 cos 2 theta-sin theta=2

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, by induction, that (cos theta + isintheta)^n = cos n theta + isin ntheta for all positive as well as negative integral values of n

Solve 2 cos^(2) theta = 3 sin theta

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

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

Which statement is correct.? bb"statement-1" (cos theta+isin theta)^(3)=cos 3theta+isin 3theta, i=sqrt(-1) bb"statement-2" (cos""pi/4+isin""pi/4)^(2)=i

Solve cos theta+cos 2theta+cos 3theta=0 .

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