若sinA+cosA/sinA-cosA=2,则sin(A-5π)*sin(7π/2-A)等于？？

显示全部楼层 · 2013-2-23 10:04:48

（sina+cosa)/(sina-cosa)=2所以sina=3cosa因为sina*sina+cosa*cosa=1,所以sina=3*根号10/10，cosa=根号10/10，或者sina=-3*根号10/10，cosa=-根号10/10；sin(A-5π)*sin(7π/2-A)=(-sinA)*(-sin(A+π/2)=sina*cosa=3/10...

千问 · 2013-2-23 10:04:48

sinA+cosA/sinA-cosA=2tanA=3sin(A-5π)*sin(7π/2-A)=-sinA*sin[4π-(π/2+A)]=sinA*sin(π/2+A)=sinAcosA=1/2sin2A=1/2*2tanA/(1+tan^2A)=tanA/(1+tan^2A)=3/(1+9)=3/10...

千问 · 2013-2-23 10:04:48

(sinA+cosA)/(sinA-cosA)=2sinA+cosA=2sinA-2cosA3cosA=sinAsin2A+cos2A=1，9cos2A+cos2A=1，cos2A=1/10sin(A-5π)*sin(7π/2-A)=(-sin(5π-A)sin(2π+3π/2-A)=...