How many x ∈ ( − π , π ) satisfy 81 ( 1 + ∣ sin x ∣ + ∣ sin x ∣ 2 + ⋯ ) = 3 8 ?

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MathematicsTrigonometric EquationTrigonometric EquationMedium3 minQB

MathematicsMediuminteger

How many $x \in (- π, π)$ satisfy $81 (1 + ∣ sin x ∣ + ∣ sin x ∣^{2} + \dots) = 3^{8}$ ?

Answer:

Solution:

The series equals 2, so $∣ sin x ∣ = 1/2$ . There are four such values in ( $- π, π$ ).

Stream:JEESubject:MathematicsTopic:Trigonometric EquationSubtopic:Trigonometric Equation

⏱ 3mℹ️ Source: QB

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