If sin-13-x - sin-14-x-2- then x-

Explanation for the correct option.Given that, sin^ 13/x + sin^ 14/x=π/2Using identity, sin^ 1x+cos^ 1x=π/2.⇒sin^ 13/x=cos^ 14/x0ex0ex⇒sin^ 13/x=sin^ 1√(x^2 16) ...

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Standard XII

Mathematics

Rationalization Method to Remove Indeterminate Form

If sin-13/x +...

Question

If $\sin^{- 1} \frac{3}{x} + \sin^{- 1} \frac{4}{x} = \frac{π}{2}$ , then $x =$

$3$

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$5$

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$7$

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$11$

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Solution

The correct option is B
$5$

Explanation for the correct option.
Given that, $\sin^{- 1} \frac{3}{x} + \sin^{- 1} \frac{4}{x} = \frac{π}{2}$
Using identity, $\sin^{- 1} x + \cos^{- 1} x = \frac{π}{2}$ .
$\Rightarrow \sin^{- 1} \frac{3}{x} = \cos^{- 1} \frac{4}{x} \Rightarrow \sin^{- 1} \frac{3}{x} = \sin^{- 1} \frac{\sqrt{x^{2} - 16}}{x} \Rightarrow \frac{3}{x} = \frac{\sqrt{x^{2} - 16}}{x} \Rightarrow 9 = x^{2} - 16 \Rightarrow x^{2} = 25 \Rightarrow x = \pm 5$
Hence option B is correct.

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If sin-13x+sin-14x=π2, then x=

The correct option is B 5Explanation for the correct option.Given that, sin-13x+sin-14x=π2Using identity, sin-1x+cos-1x=π2.⇒sin-13x=cos-14x⇒sin-13x=sin-1x2-16x⇒3x=x2-16x⇒9=x2-16⇒x2=25⇒x=±5Hence option B is correct.

If $\sin^{- 1} \frac{3}{x} + \sin^{- 1} \frac{4}{x} = \frac{π}{2}$ , then $x =$