已知tan(π/4+θ)=2,求sin2θ+cos2θ+1的值.

tan(π/4+θ)
=(tanπ/4+tanθ)/(1-tanπ/4tanθ)
=(1+tanθ)/(1-tanθ)
=2
由此可以解出 tan θ= 1/3.
万能公式
cos2θ＝(1-tan^θ)/(1+tan^θ)
sin2θ＝ 2tanθ/(1+tan^θ)
cos2θ+sin2θ
=(1-tan^θ)/(1+tan^θ) +2tanθ/(1+tan^θ)
=(1-tan^θ+2tanθ)/(1+tan^θ)
=[1-1/9+2*1/3]/(1+1/9)
=7/5
sin2θ+cos2θ+1=7/5+1=12/5
^表平方