Question

已知tan（π/4+x）=3,求sin2x-2cos^2x的值（要解答过程哦~）

Answer 1

tan(x+45)=(tanx+tan45)/(1-tanxtan45)=3所以tanx+1=3-3tanxtanx=0.5有万能公式sin2x=2tanx/(1+tanxtanx)=2*0.5/(1+0.5*0.5)=1/(1.25)=4/5cos2x=(1-tanxtanx)/(1+tanxtanx)=(1-0.25)/(1+0.25)=0.75/1.25=3/5sin2x-2cos^2x=sin2x-2cos^2x+1-1=sin2x-1-(2cos^2x-1)=sin2x-1-cos2x=4/5-1-3/5=-4/5哪里不清请追问,