Question

Find $\underset{x\to 0}{lim}\frac{1-\cos 4\theta }{1-\cos 6\theta }$

Answer 1

$\underset{x\to 0}{lim}\frac{1-\cos 4\theta }{1-\cos 6\theta }$

$=\underset{x\to 0}{lim}\frac{1-\cos 4\theta }{1-\cos 6\theta }$

$=\underset{x\to 0}{lim}\frac{2{\cos }^{2}2\theta }{2{\cos }^{2}3\theta }$

$=\underset{x\to 0}{lim}\frac{{\cos }^{2}2\theta }{{\cos }^{2}3\theta }$

$=\frac{1}{1}=1$