If 2 ^ - 1 1 + x 2 = 2 , then x = - Vidyadip

Question

If $2{\cos ^{ - 1}}\sqrt {\frac{{1 + x}}{2}} = \frac{\pi }{2},$ then $x = $

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Answer

b
(b) Given equation is $2{\cos ^{ - 1}}\sqrt {\left( {\frac{{1 + x}}{2}} \right)} = \frac{\pi }{2}$

==> ${\cos ^{ - 1}}\sqrt {\left( {\frac{{1 + x}}{2}} \right)} = \frac{\pi }{4} $

$\Rightarrow \cos \frac{\pi }{4} = \frac{{\sqrt {1 + x} }}{{\sqrt 2 }}$

==> $\frac{1}{{\sqrt 2 }} = \frac{{\sqrt {1 + x} }}{{\sqrt 2 }} $

$\Rightarrow 1 = \sqrt {1 + x} \Rightarrow x = 0$.

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