Let-be-an-acute-angle-such-that-the-equation-x-2-4xcos-cot-0-involving-variable-x-has-multiple-roots-Then-the-measure-of-in-radians-is-

Question Number 144800 by imjagoll last updated on 29/Jun/21

Let β be an acute angle such

that the equation x^{2} + 4 xcos β + \cot β = 0

involving variable x has multiple

roots . Then the measure of β in

radians is__

Answered by liberty last updated on 29/Jun/21

since the equation x^{2} + 4 x \cos β + \cot β = 0

has multiple roots, we have

△ = 0 \to 16 \cos^{2} β - 4 \cot β = 0

\to 4 \cot β (2 \sin 2 β - 1) = 0

when 0 < β < \frac{π}{2} we get

\sin 2 β = \frac{1}{2} so {\begin{cases} β = \frac{π}{12} or \\ β = \frac{5 π}{12} \end{cases} .

Facebook Tweet Pin