If cos-1x-cos-1y-cos-1z -3 - then x2 -y2 -z2 -xy -yz -zx equals to

Since maximum value of cos^ 1x is π Therefore, cos^ 1x+cos^ 1y +cos^ 1z =3π⇒ cos^ 1x =cos^ 1y =cos^ 1z=π ⇒ x=y =z= 1 ⇒ x^2 +y^2+z^2 xy yz zx =0 ...

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Properties Derived from Trigonometric Identities

If cos-1x+cos...

Question

If $c o s^{- 1} x + c o s^{- 1} y + c o s^{- 1} z = 3 π t h e n x^{2} + y^{2} + z^{2} - x y - y z - z x$ equals to

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Similar questions

c o s^{- 1} x + c o s^{- 1} y + c o s^{- 1} z = 3 π

x y + y z + z x =

cos^{- 1} x + cos^{- 1} y + {cos}^{- 1} z = 3 π

x y + y z + z x

c o s^{- 1} x + c o s^{- 1} y + c o s^{- 1} z = π

x^{2} + y^{2} + z^{2} + 2 x y z

{s i n}^{- 1} x, {c o s}^{- 1} x, {t a n}^{- 1} x

{t a n}^{- 1} x + {t a n}^{- 1} y = {t a n}^{- 1} \frac{x + y}{1 - x y}

x y < 1

π + {t a n}^{- 1} \frac{x + y}{1 - x y}

x y > 1

{c o s}^{- 1} p + {c o s}^{- 1} q + {c o s}^{- 1} r = π

p^{2} + q^{2} + r^{2} + 2 p q r = 1

{s i n}^{- 1} x + {s i n}^{- 1} y + {s i n}^{- 1} z = π

x^{4} + y^{4} + z^{4} + 4 x^{2} y^{2} z^{2} = 2 (x^{2} y^{2} + y^{2} z^{2} + z^{2} x^{2})

{t a n}^{- 1} x + {t a n}^{- 1} y + {t a n}^{- 1} z = π

π / 2

x + y + z = x y z

x y + y z + z x = 1

{cos}^{- 1} x + {cos}^{- 1} y + {cos}^{- 1} z = 3 π

\sum x y

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