三角函数高一两小题

(1)sin x/2 - 2cos x/2 =0 1式
(sin x/2 )^2- (cos x/2)^2 =1 2式
由1式和2式联立得
sin x/2=2根5 cos x/2 =根5
或sin x/2=-2根5 cos x/2 =-根5
tan x/2=(sin x/2)/(cos x/2)=2
tanx=(2tan x/2)/(1-(tan x/2)^2)=-4/3
(2)cos2x/√(2)cos(π/4+x)*sinx
=(2(cos x)^2-1)/(根2(cos(π/4)cos x-sin(π/4)sin x))*sinx
=(2(cos x)^2-1)/(cos x-sin x)*sin x
因为sin x/2=2根5 cos x/2 =根5
或sin x/2=-2根5 cos x/2 =-根5
所以(2(cos x)^2-1)/(cos x-sin x)*sin x
=(2(根5)^2-1)/(根5-2根5)*2根5或(2(-根5)^2-1)/(-根5-(-2根5))*-2根5
=-18