已知tan θ
已知tan θ -1/tan θ=-4,求tan(π/4 +2θ)的值.
因为tan θ -1/tan θ=-4 所以1-(tanθ)^2=4tan θ tan2θ=2tan θ/(1-(tan θ)^2)=2tan θ/(4tan θ)=1/2 tan(π/4 +2θ)=(1+tan2θ)/(1-tan2θ)=3
tant-1/tant=-4--->(tant)^2-1=-4tant --->4tant/[1-(tant)^2]=1 --->tan2t=1/2 tan(2t+pi/4)=(1+tan2t)/(1-tan2t)=(1+1/2)/(1-1/2)=3
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