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Question Number 195315 by cortano12 last updated on 30/Jul/23

$$⋐$$

Answered by horsebrand11 last updated on 30/Jul/23

$$=\underset{x\to 0}{\lim }\frac{\tan {}^2\mathrm{a}-\tan {}^2\mathrm{x}-\tan {}^2\mathrm{a}+\tan {}^4\mathrm{a}\tan {}^2\mathrm{x}}{{\mathrm{x}}^2(1-\tan {}^2\mathrm{a}\tan {}^2\mathrm{x})}$$$$=\underset{x\to 0}{\lim }\frac{-\tan {}^2\mathrm{x}(1-\tan {}^4\mathrm{a})}{{\mathrm{x}}^2(1-\tan {}^2\mathrm{a}\tan {}^2\mathrm{x})}$$$$=\overline{)\begin{array}{c}-\frac{1-\tan {}^4\mathrm{a}}{1-\tan {}^4\mathrm{a}}=-1\end{array}}$$

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