Question

已知cos（x+45º)=3／5且17π/12＜x＜7π/4,求sin2x+2sin²x／1-tan

Answer 1

原式化为Sin2x(Cosx+Sinx)/(Cosx-Sinx)

x+(π/4)的Cos值为0.6,那么由x范围确定x+(π/4)为第4象限角,

则sin(x+45°）=-0.8,由和角公式跟倍角公式确定Cos(2x+90°)=-0.28,则Sin2x=0.28

(cosx+sinx)=-4*(2^½)/5

(cosx-sinx)=3*(2^½)/5

带入原式=-28/75