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Question
The number of real solutions of the equation `sqrt(1 + cos 2x) = sqrt(2) cos^-1 (cos x)` in `[pi/2, pi]` is ______.
Options
0
1
2
Infinite
Solution
The number of real solutions of the equation `sqrt(1 + cos 2x) = sqrt(2) cos^-1 (cos x)` in `[pi/2, pi]` is infinite.
Explanation:
We have `sqrt(1 + cos 2x) = sqrt(2) cos^-1 (cos x)`
⇒ `sqrt(2 cos^2x) = sqrt(2)x` .....`[because cos^-1 (cos x) = x]`
⇒ `sqrt(2) cos x = sqrt(2)x`
⇒ cos x = x
Which does not satisfy for any value of x.
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