`(1)/(cos theta-isin theta)` Find modulus

State true or false: If z= (cos2theta+isin2theta)/(costheta+isintheta) then z is unimodular.

If ((4i^(3)-i)/(2i+1))^(2)=r(cos theta+isin theta) , then cos theta+sin theta is equal to (where, i^(2)=-1 )

Modulus of (cos theta-isin theta)/(sin theta-icos theta) is

What is the modulus of the complex number (cos theta+i sin theta)/(cos theta-i sin theta) where i=sqrt(-1) ?

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

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)

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))

Find the characteristic roots of the two-rowed orthogonal matrix [(cos theta,-sin theta),(sin theta,cos theta)] and verify that they are of unit modulus.

A = [(cos theta,-sin theta),(-sin theta,-cos theta)] then find A^(-1) .