The number of real solutions of the equation -1-cos 2x-2 sin-1sin x - - x- is

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The number of...

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The number of real solution(s) of the equation $\sqrt{1 + cos 2 x} = \sqrt{2} {sin}^{- 1} (sin x), - π \leq x \leq π$ is

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\sqrt{1 + cos 2 x} = \sqrt{2} {sin}^{- 1} (sin x)

x \in [- π, π]

{sin}^{- 1} (\infty \sum i = 1 x^{i + 1} - x \infty \sum i = 1 {(\frac{x}{2})}^{i}) = \frac{π}{2} - {cos}^{- 1} (\infty \sum i = 1 {(- \frac{x}{2})}^{i} - \infty \sum i = 1 (- x)^{i})

(- \frac{1}{2}, \frac{1}{2})

{sin}^{- 1} x

{cos}^{- 1} x

[- \frac{π}{2}, \frac{π}{2}]

[0, π]

The number of real solutions of the equation $t a n^{- 1} \sqrt{x (x + 1)} + s i n^{- 1} \sqrt{x^{2} + x + 1} = \frac{π}{2}$ is

\sqrt{1 - c o s 2 x} = \sqrt{2} s i n^{- 1} (s i n x), - π < x \leq π

{sin}^{- 1} (\infty \sum i = 1 x^{i + 1} - x \infty \sum i = 1 {(\frac{x}{2})}^{i}) = \frac{π}{2} - {cos}^{- 1} (\infty \sum i = 1 {(- \frac{x}{2})}^{i} - \infty \sum i = 1 (- x)^{i})

(- \frac{1}{2}, \frac{1}{2})

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