Question

已知tαnα=-2+求sin^2a+2/sin^2a-cos^2a的值

Answer 1

问：已知tαnα=-2+求sin^2a+2/sin^2a-cos^2a的值

答：亲~tana=sina/cosa=-2; sina=-2cosa;sin2+cos²a=4cos2a+cos2a=1;cos²a=1/5; sin²a=4/5;.sin²a-2cos2a=4/5-2/5=2/5

答：tan(α+β)=sin(α+β)/cos(α+β)=-2 (1)tan(α-β)=sin(α-β)/cos(α-β)=1/2 (2)(1)/(2)sin(α+β)cos(α-β)/cos(α+β)sin(α-β)=-4sin2α/sin2β=sin[(α+β)+(α-β)]/sin[(α+β)-(α-β)]=[sin(α+β)cos(α-β)+cos(α+β)sin(α-β)]/[sin(α+β)cos(α-β)-cos(α+β)sin(α-β)](上下同除以cos(α+β)sin(α-β))