tng(𝛑/9) + 4sin(𝛑/9) =(√3)


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Question Number 99869 by bachamohamed last updated on 23/Jun/20

$t n g \frac{π}{9} + 4 s i n \frac{π}{9} = \sqrt{3}$
	Answered by smridha last updated on 23/Jun/20

	$\frac{s i n (\frac{π}{9}) + 2 s i n (\frac{2 π}{9})}{c o s (\frac{π}{9})} = \frac{s i n (\frac{2 π}{9}) + c o s (\frac{π}{18})}{c o s (\frac{π}{9})}$ $= \frac{s i n (\frac{4 π}{9}) + s i n (\frac{2 π}{9})}{c o s (\frac{π}{9})} = \frac{2 . \frac{\sqrt{3}}{2} . c o s (\frac{π}{9})}{c o s (\frac{π}{9})} = \sqrt{3}$
	Answered by Dwaipayan Shikari last updated on 23/Jun/20

	$T a k i n g \frac{π}{9} a s 20 °$ $\frac{1}{c o s 20 °} [4 s i n 20 ° c o s 20 ° + s i n 20 °]$ $= \frac{1}{c o s 20 °} [2 s i n 40 ° + s i n 20 °]$ $= \frac{1}{c o s 20 °} [s i n 40 ° + s i n 80 °]$ $= \frac{1}{c o s 20 °} [2 s i n 60 ° c o s 20 °] = \sqrt{3} [p r o v e d]$
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