`(2 sin theta * tan theta (1- tan theta ) + 2 sin theta sec^(2) theta )/( (1+ tan theta)^(2))=`

(2sin theta tan theta(1-tan theta)+2sin theta sec^(2)theta)/((1+tan theta)^(2))=(2sin theta)/(1+tan theta)

(2sin theta*tan theta(1-tan theta)+2sin theta*sec^(2)theta)/((1+tan theta)^(2))=(2sin theta)/(1+tan theta)

sin 2 theta * (tan theta + cot theta)= A) sec theta B) csc theta C)1D)2

(sec theta-tan theta)^2 (1+sin theta)^2 div sin^2 theta

(cos theta-sin theta) / (cos theta + sin theta) = sec2 theta-tan2 theta

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

Prove that (sin theta - cos theta + 1)/(sin theta + cos theta - 1) = (1)/(sec theta - tan theta) using the identity sec^(2) theta = 1 + tan^(2) theta .

prove that :(1-sin2 theta)/(1+sin2 theta)=((1-tan theta)/(1+tan theta))^(2)