Show that: `sin^(3) alpha + sin^(3) (120^(@) + alpha) + sin^(3) (240^(@) + alpha)= - 3/4 sin 3 alpha`

Prove that, sin^(2) alpha + sin^(2) (120^(@) - alpha) + sin^(2) (120^(@) + alpha) = 3/2

Prove that sin^(3)alpha+sin^(3)(120^(@)+alpha)+sin^(3)(240^(@)+alpha)=-(3)/(4)sin3 alpha

Prove that sin alpha + sin (120^(@) + alpha) + sin(240^(@)+ alpha)=0

Show that sin^3alpha+sin^3(120^@+alpha)+sin^3(240^@+alpha)=-3/4sin3alpha

If p sin alpha = q sin (120^(@) + alpha) = r sin (240^(@) + alpha),"prove that", pq + qr +rp = 0

Prove that, 1/3 ( cos^(3) alpha sin 3 alpha + sin^(3) alpha cos 3 alpha) = 1/4 sin 4 alpha

sin alpha * sin (60-alpha) sin (60 + alpha) = (1) / (4) * sin3 alpha

Prove that, 3[sin^(4)((3pi)/2 - alpha) + sin^(4)(3pi + alpha)] - 2[sin^(6)((pi)/2 + alpha) + sin^(6) (5pi - alpha)] = 1

sin 3 alpha = 4 sin alpha sin(x + alpha) sin(x-alpha)

If p sin alpha=q sin(120^(@)+alpha)=r sin(240^(@)+alpha) ,prove that ,pq+qr+rp=0