The sum of the solutions of the equation2 sin-1x2-x-1 - cos-1x2-x - 3-2 is

0≤x2+x+1≤1 nbsp;and nbsp;0≤x2+x≤1∴ nbsp;x nbsp;= nbsp; 1, nbsp;0 For nbsp;x nbsp;= nbsp; 1,L.H.S. nbsp;= nbsp;2 nbsp;sin 1 nbsp;1 n ...

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Properties Derived from Trigonometric Identities

The sum of th...

Question

The sum of the solutions of the equation
$2 {sin}^{- 1} (\sqrt{x^{2} + x + 1}) + {cos}^{- 1} (\sqrt{x^{2} + x}) = \frac{3 π}{2} is$

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2 {sin}^{- 1} (\sqrt{x^{2} + x + 1}) + {cos}^{- 1} (\sqrt{x^{2} + x}) = \frac{3 π}{2} is

{cos}^{- 1} (x^{2} + \frac{1}{x^{2}} - 1) + {sin}^{- 1} (x^{2} - \frac{1}{x^{2}}) + {tan}^{- 1} (x^{2})

(where x \in R - {0})

{({sin}^{- 1} x)}^{2} - {({cos}^{- 1} x)}^{2} = a; 0 < x < 1, a \neq 0

2 x^{2} - 1

{({sin}^{- 1} x)}^{2} + {({sin}^{- 1} y)}^{2} + {({sin}^{- 1} z)}^{2} = \frac{3 π^{2}}{4}

x + y + z

({sin}^{- 1} x)^{2} + ({cos}^{- 1} x)^{2} = \frac{17 π^{2}}{36}

x

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