`(cos theta + isin theta)/(cos theta - isin 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)

int cos2 theta * ln ((cos theta + sin theta) / (cos theta-sin theta)) d theta

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

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

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

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))

Evaluate: int cos2 theta ln((cos theta+sin theta)/(cos theta-sin theta))d theta

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

If 2 - cos^(2) theta = 3 sin theta cos theta , sin theta ne cos theta then tan theta is