The equation $$cos$$−$$1$$⁡α−θα−β$$=$$$$sin$$−$$1$$⁡θ−βα−β is valid for

Correct option is 3α > θ > β or α < θ < β

Questions

The equation $\cos^{- 1} \sqrt{\frac{α - θ}{α - β}} = \sin^{- 1} \sqrt{\frac{θ - β}{α - β}}$ is valid for

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α > β and θ takes any value

α = θ = β

α > θ > β or α < θ < β

none of these.

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detailed solution

Correct option is C

The given equation is valid if α−θα−β>0 and θ−βα−β>0⇒ Either α>θ>β or α<θ<β

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The equation cos−1⁡α−θα−β=sin−1⁡θ−βα−β is valid for

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The equation $\cos^{- 1} \sqrt{\frac{α - θ}{α - β}} = \sin^{- 1} \sqrt{\frac{θ - β}{α - β}}$ is valid for