A point P (- 4,3) cos (π / 2 + α) sin (- π - α) / cos (11 π / 2 - α) sin (9 π / 2 + α) on the terminal edge of known angle α

A point P (- 4,3) cos (π / 2 + α) sin (- π - α) / cos (11 π / 2 - α) sin (9 π / 2 + α) on the terminal edge of known angle α

cos（π/2＋α）sin（－π－α）/cos（11π/2－α）sin（9π/2＋α）
=-sina*sina/(-sina)cosa
=tana
tana=/4/3
cos（π/2＋α）sin（－π－α）/cos（11π/2－α）sin（9π/2＋α）=-4/3

Given cos2a + sin2a (2sina-1) = 2 / 5, a ∈ (π / 2, π), then the value of Tan (a + π / 4) is

∵a*b=cos2a+sina(2sina-1)=cos2a+2(sina)^2-sina
=1-2(sina)^2+2(sina)^2-sina=1-sina=2/5
∴ sina=3/5
∵π/2＜a＜π,∴cosa＜0,
Then cosa = - 4 / 5
∴tana=-3/4
∴tan(a+π/4)=(tana+tanπ/4)/(1-tana*tanπ/4)
=(tana+1)/(1-tana)
=(-3/4+1)/(1+3/4)
=1/7