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Class 12 Inverse Trigonometric Functions · Mcq Single Correct1 Marksinverse_trigonometric_equations

Class 12 Maths · Inverse Trigonometric Functions · Mcq Single Correct #17

How many real solutions of \(\sqrt{1+\cos2x}=\sqrt2\,\cos^{-1}(\cos x)\) lie in \([\pi/2,\pi]\)?
Graphs of y=x and y=|cos x| on [π/2,π], with no intersection.
Graphs of y=x and y=|cos x| on [π/2,π], with no intersection.

✅ Step-by-Step Solution

Final Answer: Option (A): 0
  1. On [π/2,π], arccos(cos x)=x and √(1+cos2x)=√2|cos x|. The equation is |cos x|=x, impossible because |cos x|≤1<π/2≤x. Thus there are zero solutions.

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