SinA➖cosA/sinA➕cosA➕sinA➕cosA/sinA➖cosA=-2/cos2A

ever hear of normal + and - signs? Why the em dashes and large + signs?

I assume you want to prove that

(SinA-cosA)/(sinA+cosA) + (sinA+cosA)/(sinA-cosA) = -2/cos2A

put it all over a common denominator and you have

(sinA-cosA)^2 + (sinA+cosA)^2
---------------------------------
(sinA+cosA)(sinA-cosA)

expand that out and it all reduces to -2/cos2A