Simplify `(sin^(2)theta)/(1+cos theta)+(sin^(2)theta)/(1-cos theta)`

What is the simplified value of [(cos^(2) theta)/(1+sin theta)- (sin^(2) theta)/(1 + cos theta)]^(2) ?

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

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

Simplify sqrt(1- sin^2theta ) + (1 cos^2theta)

Simplify [(sin theta)/(cos theta)+(cos theta)/(sin theta)]^(2)

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

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

1- (sin ^ (2) theta) / (1 + cos theta) + (1 + cos theta) / (sin theta) - (sin theta) / (1-cos theta) - (1) / (sec theta)

Simplify: (sin8 theta cos theta-sin6 theta cos3 theta)/(cos2 theta cos theta-sin3 theta sin4 theta)

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