If 0 < x < π and cos x + sin x = 2 1 , then tan x is

cos x + sin x = 2 1 ⇒ 1 + sin 2 x = 4 1 ⇒ sin 2 x = − 4 3 , so x is obtuse and 1 + t a n 2 x 2 t a n x = − 4 3 ⇒ 3 tan 2 x + 8 tan x + 3 = 0 ∴ tan x = 6 − 8 ± 64 − 36 = 3 − 4 ± 7 ∵ tan x < 0 ∴ tan x = 3 − 4 − 7

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Mathematics - Trigonometric Equation Question with Solution | TestHub

MathematicsTrigonometric EquationTrigonometric EquationMedium2 minPYQ_2006

MathematicsMediumsingle choice

If $0 < x < π$ and $cos x + sin x = \frac{1}{2}$ , then $tan x$ is

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$cos x + sin x = \frac{1}{2} \Rightarrow 1 + sin 2 x = \frac{1}{4} \Rightarrow sin 2 x = - \frac{3}{4}$ , so $x$ is obtuse and $\frac{2 t a n x}{1 + t a n ^{2} x} = - \frac{3}{4} \Rightarrow 3 tan^{2} x + 8 tan x + 3 = 0$ $∴ tan x = \frac{- 8 \pm 64 - 36}{6} = \frac{- 4 \pm 7}{3}$ $∵ tan x < 0 ∴ tan x = \frac{- 4 - 7}{3}$

Stream:JEESubject:MathematicsTopic:Trigonometric EquationSubtopic:Trigonometric Equation

⏱ 2mℹ️ Source: PYQ_2006

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