If $$cos$$−$$1$$⁡α$$+$$$$cos$$−$$1$$⁡β$$+$$$$cos$$−$$1$$⁡γ$$=3$$π , then α$$($$β$$+$$γ$$)+$$β$$($$γ$$+$$α$$)+$$γ$$($$α$$+$$β$$)$$ equals

Question

If $$cos$$−$$1$$⁡α$$+$$$$cos$$−$$1$$⁡β$$+$$$$cos$$−$$1$$⁡γ$$=3$$π , then α$$($$β$$+$$γ$$)+$$β$$($$γ$$+$$α$$)+$$γ$$($$α$$+$$β$$)$$ equals

Infinity Learn · Accepted Answer

We have, $$cos$$−$$1$$⁡α$$+$$$$cos$$−$$1$$⁡β$$+$$$$cos$$−$$1$$⁡γ$$=3$$π We know that, $$0$$≤$$cos$$−$$1$$⁡x≤π⇒$$cos$$−$$1$$⁡α$$+$$$$cos$$−$$1$$⁡β$$+$$$$cos$$−$$1$$⁡γ$$=3$$π is possible if and only if $$cos$$−$$1$$⁡α$$=$$$$cos$$−$$1$$⁡β$$=$$$$cos$$−$$1$$⁡γ$$=$$π⇒α$$=$$β$$=$$γ$$=$$−$$1$$∴α$$($$β$$+$$γ$$)+$$β$$($$γ$$+$$α$$)+$$γ$$($$α$$+$$β$$)=$$−$$1($$−$$1$$−$$1)$$−$$1($$−$$1$$−$$1)$$−$$1($$−$$1$$−$$1)=6$$

$If \cos^{- 1} α + \cos^{- 1} β + \cos^{- 1} γ = 3 π, then α (β + γ) + β (γ + α) + γ (α + β) equals$

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If cos−1⁡α+cos−1⁡β+cos−1⁡γ=3π , then α(β+γ)+β(γ+α)+γ(α+β) equals

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$If \cos^{- 1} α + \cos^{- 1} β + \cos^{- 1} γ = 3 π, then α (β + γ) + β (γ + α) + γ (α + β) equals$