The sum of all the roots of the equ...
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The sum of all the roots of the equation 6 sin2 x + sin x-1=0 in xe 0,21tis (A) I (B) 211 (C) 31 (D) 41

JEE/Engineering Exams
Maths
Solution
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( sin ^{2} x+sin x-1=0 ) ( 6 sin ^{2} x+3 sin x-2 sin x-1=0 ) ( 3 sin x(2 sin x+1)-1(2 sin x+1)=0 ) ( (2 sin x+1)(3 sin x-1)=0 ) ( 2 sin x+1=0 quad g quad sin x=frac{1}{3} ) ( sin x=-frac{1}{2} quad x-sin ^{-1} frac{1}{3} ) ( x=frac{pi}{9}+frac{pi}{3}=frac{4 pi}{3} ) ( 2 pi-frac{pi}{3}=frac{5 pi}{3} ) Swm the roots, [ frac{4 pi}{3}+frac{5 pi}{3}=frac{9 pi}{3}=frac{3 pi}{5} ]
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