Question

关于两角和与两角差的三角函数若sin x/2- cos x/2=1/3,则sin x=?

Answer 1

sin x/2- cos x/2=1/3,

(sinx/2-cosx/2)^2=1/9

sin(x/2)^2+cos(x/2)^2-2sinx/2cosx/2=1/9

sin(x/2)^2+cos(x/2)^2=1

2sinx/2cosx/2=sinx

所以

1-sinx=1/9

sin=1-1/9

=8/9