已知tanx=2 ,求M=2sinxcosx+cos^2 x+1
问题描述：
已知tanx=2 ,求M=2sinxcosx+cos^2 x+1
答
sinx/cosx = 2
sinx = 2 cosx
M = 4cos^2x+cos^2x+1 = 5cos^2x + 1 = sinn^2x+cos^2x + 1 = 2
答
M=2sinxcosx+cos^2 x+1
=(2sinxcosx+cos^2x+1)/1
=(2sinxcosx+cos^2x+sin^2x+cos^2x)/(sin^2x+cos^2x)
分子分母除以cos^2x
=(2tanx+1+tan^2x+1)/(tan^2x+1)
=(2*2+1+2^2+1)/(2^2+1)
=10/5
=2