The equation 2-x-1-3-sin- x- has

Total 6 points of intersection. No solution in [ 2, ∞) No solution in (0, 1/2) ...

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The equation ...

Question

The equation $2 | x | - 1 = 3 | sin π x |$ has

4

solutions

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No solution in

[2, \infty)

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6

solutions

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Two solutions in

(0, \frac{1}{2})

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Solution

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2 | x | - 1 = 3 | sin π x |

x \in (0, π),

sin x + 2 sin 2 x - sin 3 x = 3

{cos}^{- 1} x + {sin}^{- 1} x = \frac{11 π}{6}

x \in (0, π)

sin x + 2 sin 2 x - sin 3 x = 3

(s i n^{- 1} x)^{3} + (c o s^{- 1} x)^{3} - a π^{3} = 0

a ⩾ \frac{1}{32} .

x ϵ R, s i n^{- 1} x + c o s^{- 1} x = \frac{π}{2}

0 \leq (s i n^{- 1} x - \frac{π}{4})^{2} \leq \frac{9 π^{2}}{16}

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