已知sin(π/2-α0+2tan(3π/4)*cos(π/2+α)=0下接↓求sin^2(5π-α）-2sin（π/2+α）*cos（π/2-α）-cos^2（π+α）的值

Question

已知sin(π/2-α0+2tan(3π/4)*cos(π/2+α)=0 下接↓
求sin^2(5π-α）-2sin（π/2+α）*cos（π/2-α）-cos^2（π+α）的值

Answer 1

sin(π/2-α）+2tan(3π/4)*cos(π/2+α)=0
cosa+2×(-1)×(-sina)=0
cosa+2sina=0
tana=-1/2
cosa=-√5/2
sin^2(5π-α）-2sin（π/2+α）*cos（π/2-α）-cos^2（π+α）
=sin²a-2cosa.sina-cos²a
=1-cos²a-cosa(2sina+cosa)
=1-cos²a
=1-5/4
=-1/4