The value of (√3) cot 20°− 4 cos 20° is


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Question Number 48528 by Pk1167156@gmail.com last updated on 25/Nov/18

$The value of \sqrt{3} \cot 20 ° - 4 \cos 20 ° is$
	Answered by math1967 last updated on 25/Nov/18

	$\frac{\sqrt{3} c o s 20 - 4 c o s 20 s i n 20}{s i n 20}$ $= \frac{t a n 60 c o s 20 - 2 s i n 40}{s i n 20}$ $= \frac{\frac{s i n 60 c o s 20}{c o s 60} - 2 s i n 40}{s i n 20}$ $= \frac{2 s i n 60 \cos 20 - 2 s i n 40}{s i n 20} [\frac{1}{c o s 60} = 2]$ $= \frac{s i n (60 + 20) + \sin (60 - 20) - 2 \sin 40}{\sin 20}$ $= \frac{s i n 80 - s i n 40}{s i n 20} = \frac{2 s i n 20 c o s 60}{\sin 20} = 1 A n s$
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