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  4. Let N = log 10(√( cos 30°-1)2+√(2 tan 30°+1)2-4 sin 30°). Then N is

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Q. Let $N =\log _{10}\left(\sqrt{\left(\cos 30^{\circ}-1\right)^2}+\sqrt{\left(2 \tan 30^{\circ}+1\right)^2}-4 \sin 30^{\circ}\right)$. Then $N$ is

Continuity and Differentiability

Solution:

$\log _{10}\left(\left(1-\frac{\sqrt{3}}{2}\right)+\left(\frac{2}{\sqrt{3}}+1\right)-2\right)=\frac{2}{\sqrt{3}}-\frac{\sqrt{3}}{2}=\log _{10}\left(\frac{1}{2 \sqrt{3}}\right)$ \{negative real $\}$