Question

已知@为锐角,且sin^2@-sin@cos@-2cos^2=0 求tan@的值.求sin(@-3.14/3)

Answer 1

sin²a-sinacos-2cos²a=0

等式两边同时除以cos²a

tan²a-tana-2=0

(tana-2)(tana+1)=0

因为tana+1>0

所以tana-2=0,tana=2

sina=2/(根号5),cosa=1/(根号5)

sin(a-pi/3)

=sinacos(pi/3)-cosasin(pi/3)

=1/(根号5)-(根号3/2)(1/(根号5))

=(1-(根号3)/2)/(根号5)