The set of all x in -2 -2 satisfying - 4sin x-1 - -5 is given by

The correct option is A ( π/10,3π/10 ) | 4 sinx 1 | lt; √(5) ⇒ √(5) lt; nbsp; 4 sinx 1 lt; √(5) ⇒ √(5) + 14 lt; nbsp; si ...

The set of al...

Question

The set of all $x$ in $(- \frac{π}{2}, \frac{π}{2})$ satisfying $| 4 sin x - 1 | < \sqrt{5}$ is given by

(- \frac{π}{10}, \frac{3 π}{10})

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(\frac{π}{10}, - \frac{3 π}{10})

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(\frac{π}{10}, \frac{3 π}{10})

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None of these

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Solution

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x

(- π, π)

| 4 s i n x - 1 | < \sqrt{5}

x ϵ (- π, - \frac{k π}{10}) \cup (- \frac{π}{10}, \frac{π}{10}) \cup (\frac{k π}{10}, π)

k

t \in [- \frac{π}{2}, \frac{π}{2}]

2 sin t = \frac{1 - 2 x + 5 x^{2}}{3 x^{2} - 2 x - 1}

\forall x \in R - {- \frac{1}{3}, 1}

(- π, π)

| 4 sin x - 1 | < \sqrt{5}

x \in (- π, π)

| 4 sin x - 1 | < \sqrt{5}

(\frac{π}{2}, \frac{- π}{2})

| 4 sin x - 1 | < \sqrt{5}