Question Number 97238 by bobhans last updated on 07/Jun/20
Commented by john santu last updated on 07/Jun/20
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:^{\mathrm{2}} {x}\:\left(\mathrm{cos}\:^{\mathrm{2}} {x}−\mathrm{1}\right)}{\left(\mathrm{1}+\frac{{x}^{\mathrm{2}} }{\mathrm{4}}−\mathrm{1}\right)\left(\mathrm{1}−\frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{2}}−\mathrm{1}\right)}\:= \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{−{x}^{\mathrm{4}} }{−\frac{\mathrm{1}}{\mathrm{8}}{x}^{\mathrm{4}} }\:=\:\mathrm{8}\: \\ $$