Hi! I have to solve this limit WITHOUT using the Hospital's Rule and in the most simple way. I also have to explain the reasoning behind each and every step and specify each identity used to find the answer.

Lim (x->pi/5) (sinx-sin(pi/5))/(x-(pi/5))

I solved it with the Hospital's Rule and got cos(pi/5). However, I get no points by solving it that way. Hence, I'm completely stuck and can't figure out how to do it.