(1+sin2x)/(2cos^2x+sin2x)=1/2tanx+1/2
3个回答

(1+sin2x)/(2cos^2x+sin2x)=1/2tanx+1/2

因为sin2x=2sinxcosx,1=cosx^2+sinx^2

所以1+sin2x=cosx^2+sinx^2+2sinxcosx=(cosx+sinx)^2

2cos^2x+sin2x=2cos^2x+2sinxcosx=2cosx(cosx+sinx)

所以(1+sin2x)/(2cos^2x+sin2x)=(cosx+sinx)^2/[2cosx(cosx+sinx)]

=(cosx+sinx)/2cosx

=1/2 +1/(2tanx)