Question

lim x->0 tan(2x)csc(5x)

Answer 1

\[\tan 2x\csc 5x=\frac{\sin 2x}{\cos 2x}\cdot\frac{1}{\sin 5x}=\frac{1}{\cos 2x}\cdot 2\frac{\sin 2x}{2x}\cdot \frac{1}{5}\frac{5x}{\sin 5x}\]

Answer 2

alternative :
lim x->0 tan(2x)csc(5x) = lim x->0 tan(2x)/sin(5x)
use the basic formula : lim x->0 tan(Ax)/sin(Bx) = A/B