How to evaluate $$ \lim_{x \rightarrow \pi }\frac{\sin(7x)}{\sin(4x)}$$ surely there must be some nice trick here?
L'hopital Rule is not allowed here.
2026-04-03 19:16:35.1775243795
Evaluate the limit of $\frac{\sin(7x)}{\sin(4x)}$?
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Change variable $x=y+\pi$. So $$\frac {\sin(7x)}{\sin(4x)}=-\frac {\sin(7y)}{\sin(4y)}=-\frac 74\times\frac {\sin(7y)} {7y}\times\frac {4y} {\sin(4y)} $$
I am sure that you can take from here.