If `p sin alpha=qsin(12 0^(@)+alpha)=rsin(24 0^(@)+alpha)`, prove that, `pq + qr+rp = 0`.

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

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

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

Prove that, cos alpha + cos(120^(@) + alpha) + cos (120^(@) - alpha) = 0

prove sin alpha+sin(alpha+(2pi)/3)+sin (alpha+(4pi)/3)=0

Prove that sin alpha+sin(alpha+2pi/3)+sin(alpha+4pi/3)=0

lim_(alpha to 0) (sin (alpha^n))/((sin alpha)^(m))

If tan theta = (Q sin alpha)/(P + Q cos alpha), "prove that", tan (alpha - theta) = (P sin alpha)/(Q + P cos alpha).

If sin(120^(0)-alpha)=sin(120^(@)-beta),0

If sin alpha =(1)/(2) , prove that (3 cos alpha - 4 cos ^(3) alpha )=0.