The value of x for which sin -1sin2 x2-4-1-x2-3 is

The correct option is A ( 1, 1)sin^ 1{sin(2x^2+4/1+x^2 )} lt;π 3 ⇒π (2+2/1+x^2 ) lt;π 3 ⇒ 2/1+x^2 lt; 1 ⇒ 2 gt;1+x^2 ⇒ x^2 1 lt;0 ⇒ x ϵ ( 1,1) ...

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Byju's Answer

Standard XII

Mathematics

Solving Simultaneous Trigonometric Equations

The value of ...

Question

The value of x for which $s i n^{- 1} {s i n (\frac{2 x^{2} + 4}{1 + x^{2}})} < π - 3$ is

(o, 1)

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(-1, 0)

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(-1, 1)

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(0, 2)

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Solution

The correct option is C
(-1, 1)

$s i n^{- 1} {s i n (\frac{2 x^{2} + 4}{1 + x^{2}})} < π - 3$
$\Rightarrow π - (2 + \frac{2}{1 + x^{2}}) < π - 3$
$\Rightarrow - \frac{2}{1 + x^{2}} < - 1$
$\Rightarrow 2 > 1 + x^{2}$
$\Rightarrow x^{2} - 1 < 0$
$\Rightarrow x ϵ (- 1, 1)$

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The value of x for which sin−1{sin(2x2+41+x2)}<π−3 is

The correct option is C (-1, 1)sin−1{sin(2x2+41+x2)}<π−3 ⇒π−(2+21+x2)<π−3 ⇒−21+x2<−1 ⇒2>1+x2 ⇒x2−1<0 ⇒xϵ(−1,1)

The value of x for which $s i n^{- 1} {s i n (\frac{2 x^{2} + 4}{1 + x^{2}})} < π - 3$ is

The correct option is C
(-1, 1)

$s i n^{- 1} {s i n (\frac{2 x^{2} + 4}{1 + x^{2}})} < π - 3$
$\Rightarrow π - (2 + \frac{2}{1 + x^{2}}) < π - 3$
$\Rightarrow - \frac{2}{1 + x^{2}} < - 1$
$\Rightarrow 2 > 1 + x^{2}$
$\Rightarrow x^{2} - 1 < 0$
$\Rightarrow x ϵ (- 1, 1)$