Prove that `((1+sin theta+i cos theta)/(1+sin theta-i cos theta))^(n)=(sin theta+i cos theta)^(n)`

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

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

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

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

(1)/(cos theta-i sin theta)

(sin theta+cos theta)(1-sin theta cos theta)=sin^3 theta+cos^3 theta

Prove that (sin theta - cos theta +1)/(sin theta + cos theta -1) = (1)/((sec theta - tan theta)).

Prove: ((1+sin theta-cos theta)/(1+sin theta+cos theta))^(2)=(1-cos theta)/(1+cos theta)

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

Prove that : (1+sin2 theta-cos 2theta)/(sin theta+cos theta)=2sin theta