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The number of real solutions of the equation$\sqrt{1+\cos2x}=\sqrt 2\cos^{-1}(\cos x)\;in\begin{bmatrix}\frac{\Large \pi}{2},\pi\end{bmatrix}$

\[(A)\quad 0\quad(B)\quad 1\quad(C)\quad 2\quad(D)\quad \text{Infinite}\]
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  • \(1+cos2x=2cos^2x\)
Ans - A, no real solution.
\( \sqrt{1+cos2x} = \sqrt {2 cos^2x}=\sqrt2\:cosx \)
Substituting the value in the given eqn.
\(\Rightarrow\: \sqrt2\:cosx =\sqrt2\: x \)
\(\Rightarrow\:cosx=x,\)which does not exist for any x.


answered Feb 18, 2013 by thanvigandhi_1
edited Mar 16, 2013 by thanvigandhi_1

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