tan(x/2)=2 求cos2x+sin2x

tan(x/2)=2 求cos2x+sin2x
tan(x/2)=2 求cos2x+sin2x

tan(x/2)=2 求cos2x+sin2x
用万能公式来解题：tanx=2tan(x/2)/{1-[tan(x/2)]^2}=-4/3,cos2x=1-(tanx)^2/[1+(tanx)^2] sin2x=2tanx/[1-(tanx)^2]算出来就可以了

因为tan(x/2)=2,所以tanx=2*2/(1-2^2)=-4/3
由万能公式有sinx=2*2/(1+2^2)=4/5
cosx=(1-2^2)/(1+2^2)=-3/5
所以cos2x+sin2x
=(cosx)^2-(sinx)^2+2sinxcosx
=(-3/5)^2-(4/5)^2+2*4/5*(-3/5)
=-31/25