Question

已知sin²2a+sin2acosa-cos2a=1,a属于(0,π/2),求sina,tana

Answer 1

sin²2a+sin2acosa-cos2a=1

(2sinacosa)^2+2sina(cosa)^2-2(cosa)^2+1=1

2(cosa)^2[2(sina)^2+sina-1]=0

2(cosa)^2(sina+1)(2sina-1)=0

a属于(0,π/2),cosa>0 sina>0,因此只有sina-1/2=0 sina=1/2

tana=√3/3

sina=1/2 tana=√3/3