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

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

(1)/(sin^(2)theta)-(cos^(2)theta)/(sin^(2) theta) =___.

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

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

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

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

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

(sin theta)/(1+cos theta)+(1+cos theta)/(sin theta)=2cos ec theta

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1