0

The answer is :

$$\sin(\frac {x+x+(n-1)y}{2}) \dfrac {\sin \frac{ny}{2}}{\sin \frac {y}{2}}$$

I could've written the question as: Show that..., but then people would try induction.

What I did: $$\sin x+\sin (x+y)+ ... +\sin (x+(n-1)y)$$ $$=2\sin(x+y/2)\cos(y/2)+\sin (x+2y)+...+\sin(x+(n-1)y)$$ $$=\dfrac {sin(x+y/2)sin(y)}{\sin (y/2)}+\sin(x+2y)+...+\sin(x+(n-1)y)$$

. . . I don't think that's taking me anywhere near to a solution. Any better ideas than this(stupid one) will be appreciated. Thanks for any help.

Shubham
  • 880

0 Answers0