If cos -1 x-cos -1 y-cos -1 z-3 - then the value of x3-y3-z3-3 x y z is

The correct option is A 0cos^ 1x+cos^ 1y+cos^ 1z=3π We know 0 ≤cos^ 1x ≤π Therefore, the equation is possible only when nbsp; cos^ 1x=cos^ 1y=cos^ 1z=π nb ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

General Solution of Trigonometric Equation

If cos -1 x+c...

Question

If ${cos}^{- 1} x + {cos}^{- 1} y + {cos}^{- 1} z = 3 π,$ then the value of $x^{3} + y^{3} + z^{3} - 3 x y z$ is

0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $0$
${cos}^{- 1} x + {cos}^{- 1} y + {cos}^{- 1} z = 3 π$
$We know 0 \leq {cos}^{- 1} x \leq π$
Therefore, the equation is possible only when
${cos}^{- 1} x = {cos}^{- 1} y = {cos}^{- 1} z = π$
Thus, $x = y = z = - 1$
$∴ x^{3} + y^{3} + z^{3} - 3 x y z = 0$

Suggest Corrections

Similar questions

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

then the value of

x y + y z + z x

Q. If

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

, then value of

\sum x y

equals

Q. For

{sin}^{- 1} x + {cos}^{- 1} y + {sec}^{- 1} z \geq t^{2} - \sqrt{2 π} t + 3 π

, then the principal value of

{cos}^{- 1} (cos 5 t^{2})

is,

Q. For

{sin}^{- 1} x + {cos}^{- 1} y + {sec}^{- 1} z \geq t^{2} - \sqrt{2 π} t + 3 π

, then the value of

{cos}^{- 1} (m i n {x, y, z})

is,

Q. 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

Join BYJU'S Learning Program

If cos−1x+cos−1y+cos−1z=3π, then the value of x3+y3+z3−3xyz is

The correct option is A 0cos−1x+cos−1y+cos−1z=3π We know 0≤cos−1x≤π Therefore, the equation is possible only when cos−1x=cos−1y=cos−1z=π Thus, x=y=z=−1 ∴x3+y3+z3−3xyz=0

If ${cos}^{- 1} x + {cos}^{- 1} y + {cos}^{- 1} z = 3 π,$ then the value of $x^{3} + y^{3} + z^{3} - 3 x y z$ is

The correct option is A $0$
${cos}^{- 1} x + {cos}^{- 1} y + {cos}^{- 1} z = 3 π$
$We know 0 \leq {cos}^{- 1} x \leq π$
Therefore, the equation is possible only when
${cos}^{- 1} x = {cos}^{- 1} y = {cos}^{- 1} z = π$
Thus, $x = y = z = - 1$
$∴ x^{3} + y^{3} + z^{3} - 3 x y z = 0$