已知cos（四分之派+X）=五分之三,十二分之十七π小于X小于四分之七π,求1-tanx分之sin2x+2倍sin方X

Question

已知cos（四分之派+X）=五分之三,十二分之十七π小于X小于四分之七π,求1-tanx分之sin 2x+2倍sin方X

Answer 1

cos(π/4+x)=3/5,
∴sin2x=-cos[2(π/4+x)]=-[2*(3/5)^2-1]=7/25,
17π/12∴5π/3∴sin(π/4+x)=-4/5.
[sin2x+2(sinx)^2]/(1-tanx)
=[2sinxcosx+2(sinx)^2]/(1-sinx/cosx)
=2sinxcosx(cosx+sinx)/(cosx-sinx)
=sin2xsin(π/4+x)/cos(π/4+x)
=(7/25)*(-4/5)/(3/5)
=-28/75.