if `3/(2+cos theta+i sin theta)=a+ib` then prove that `a^2+b^2=4a-3`

If z = (3)/( 2 + cos theta + I sin theta) , then prove that z lies on the circle.

If cos theta + sin theta =sqrt(2) cos theta prove that cos theta -sin theta =sqrt(2) sin theta

Express 1/(1+cos theta-i sin theta) in the form of a +ib .

If x = 2 cos theta - cos 2theta and y = 2 sin theta - sin 2theta then prove that : (dy)/(dx)=tan (3 theta)/(2)

One of the general solutions of sqrt(3) cos theta -3 sin theta =4 sin 2 theta cos 3 theta is

sin^(3)theta + sin theta - sin theta cos^(2)theta =

Solve : 3-2 cos theta -4 sin theta - cos 2theta+sin 2theta=0 .

Solve sqrt(3) cos theta-3 sin theta =4 sin 2 theta cos 3 theta .

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))

Solve 7cos^2theta+3sin^2theta=4