look at the attachment
Simplified it too
pls take it seriously

[tex]\\ \rm\rightarrowtail \dfrac{sin(180+A)+2cos(180+A).cos(A-180)}{2cos^2(360+A)-cos(-A)}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{-sinA+2(cos^2A-sin^2A)}{2cos^2A-cosA}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{-sinA+2cos^2A-2sin^2A}{cosA(2cosA-1)}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{-sinA+2-2sin^2A-2sin^2A}{cosA(2cosA-1)}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{-sinA-4sin^2A}{cosA(2cosA-1)}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{-sinA(4sinA-1)}{cosA(2cosA-1)}[/tex]
[tex]\\ \rm\rightarrowtail -tanA\left(\dfrac{4sinA-1}{2cosA-1}\right)[/tex]