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

Answer 1

The number of real solutions of the equation `sqrt(1 + cos 2x) = sqrt(2) cos^-1 (cos x)` in `[pi/2, pi]` is 0.

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

∴ There are no solution for given equation.