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Q)

If for real values of $x\cos\theta=x+\large\frac{1}{x}$,then

$\begin{array}{1 1}(A)\;\theta\text{ is an acute angle}\\(B)\;\theta\text{ is right angle}\\(C)\;\theta\text{ is an obtuse angle}\\(D)\;\text{No value of }\theta\text{ is possible}\end{array}$

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A)
$y=\cos^{-1}x\quad(-1 \leq x \leq 1)$
Given :
$\cos\theta=x+\large\frac{1}{x}$
$\cos \theta=\large\frac{x^2+1}{x}$
$\theta \geq 1$ or $\theta \leq -1$
It is not possible.
Hence (D) is the correct answer.

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A)
If for real valu of x cos theta=x+1/x