If x3-x - 2- then the value of sin -1x-sin -1x2-sin -1x3-sin -1x10 is

X(3 x) ≥ 2 ⇒ 3 x x^2≥ 2 ⇒ x^2 3 x+2 ≤ 0 ⇒ (x 1)(x 2) ≤ 0 ⇒x∈[1,2] But the domain of sin ^ 1 x is [ 1,1] ∴ x=1 sin ^ 1(x)+sin ^ 1(x^2)+sin ^ 1(x^3)+⋯+sin ^ 1(x^ ...

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Standard VI

Mathematics

Idea of a Set

If x3-x ≥ 2, ...

Question

If $x (3 - x) \geq 2$ , then the value of ${sin}^{- 1} (x) + {sin}^{- 1} (x^{2}) + {sin}^{- 1} (x^{3}) + \dots + {sin}^{- 1} (x^{10})$ is

\frac{π}{2}

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2 π

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5 π

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10 π

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Solution

The correct option is C $5 π$
$x (3 - x) \geq 2$
$\Rightarrow 3 x - x^{2} \geq 2$
$\Rightarrow x^{2} - 3 x + 2 \leq 0$
$\Rightarrow (x - 1) (x - 2) \leq 0$
$\Rightarrow x \in [1, 2]$
But the domain of ${sin}^{- 1} x$ is $[- 1, 1]$
$∴ x = 1$

${sin}^{- 1} (x) + {sin}^{- 1} (x^{2}) + {sin}^{- 1} (x^{3}) + \dots + {sin}^{- 1} (x^{10})$
$= \frac{π}{2} + \frac{π}{2} + \dots + \frac{π}{2} (10 times)$
$= 5 π$

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Standard VI Mathematics

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If x(3−x)≥2, then the value of sin−1(x)+sin−1(x2)+sin−1(x3)+⋯+sin−1(x10) is

The correct option is C 5πx(3−x)≥2 ⇒3x−x2≥2 ⇒x2−3x+2≤0 ⇒(x−1)(x−2)≤0 ⇒x∈[1,2] But the domain of sin−1x is [−1,1] ∴x=1 sin−1(x)+sin−1(x2)+sin−1(x3)+⋯+sin−1(x10) =π2+π2+⋯+π2 (10 times) =5π

If $x (3 - x) \geq 2$ , then the value of ${sin}^{- 1} (x) + {sin}^{- 1} (x^{2}) + {sin}^{- 1} (x^{3}) + \dots + {sin}^{- 1} (x^{10})$ is