已知tanx=2 ,求M=2sinxcosx+cos^2 x+1

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已知tanx=2,求M=2sinxcosx+cos^2x+1已知tanx=2,求M=2sinxcosx+cos^2x+1已知tanx=2,求M=2sinxcosx+cos^2x+1M=2sinxcos

已知tanx=2 ,求M=2sinxcosx+cos^2 x+1
已知tanx=2 ,求M=2sinxcosx+cos^2 x+1

已知tanx=2 ,求M=2sinxcosx+cos^2 x+1
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

sinx/cosx = 2
sinx = 2 cosx
M = 4cos^2x+cos^2x+1 = 5cos^2x + 1 = sinn^2x+cos^2x + 1 = 2