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Question Number 206020 by NANIGOPAL last updated on 05/Apr/24

Answered by cortano12 last updated on 05/Apr/24

$$=\underset{x\to 0}{\lim }\frac{x(\frac{2\tan x}{1-\tan {}^{2}x}-2\tan x)}{4\sin {}^{4}x}$$$$=\underset{x\to 0}{\lim }\frac{2x\tan x(1-(1-\tan {}^{2}x))}{4\sin {}^{4}x}$$$$=\frac{1}{2}\underset{x\to 0}{\lim }\frac{\tan {}^{2}x}{\sin {}^{2}x}=\frac{1}{2}$$

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