Question

化简：sin方（a-30°）+sin方（a+30°）—sin方a

Answer 1

sin^2(a-30°)+sin^2(a+30°)-sin^2a

=(sinacos30°-cosasin30°)^2+(sinacos30°+cosasin30°)^2-sin^2a

=(√3/2*sina-1/2*cosa)^2+(√3/2*sina+1/2*cosa)^2-sin^2a

=3/2*sin^2a+1/2*cos^2-sin^2a

=1/2*sin^2a+1/2*cos^2a

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

=1/2.