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Question-118065




Question Number 118065 by andilizhaa last updated on 15/Oct/20
Answered by bobhans last updated on 15/Oct/20
f(x)=1−cot x  ((df(x))/dx) = cosec^2 (x)  ((df(x))/dx)∣_(π/6)  = (1/(sin^2 ((π/6)))) = 4
$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{1}−\mathrm{cot}\:\mathrm{x} \\ $$$$\frac{\mathrm{df}\left(\mathrm{x}\right)}{\mathrm{dx}}\:=\:\mathrm{cosec}\:^{\mathrm{2}} \left(\mathrm{x}\right) \\ $$$$\frac{\mathrm{df}\left(\mathrm{x}\right)}{\mathrm{dx}}\mid_{\frac{\pi}{\mathrm{6}}} \:=\:\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\pi}{\mathrm{6}}\right)}\:=\:\mathrm{4} \\ $$

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