If cos -1 x-cos -1 y-cos -1 z-3 - then x y-y z-z x-

The correct option is C 3Given cos^ 1x+cos^ 1y+cos^ 1z=3π ∵ 0≤ cos^ 1x ≤π ∴ 0 ≤ cos^ 1y ≤π and 0 ≤ cos^ 1z ≤π Here cos^ 1 x=cos^ 1y=cos^ 1z=π ⇒ x=y=z=cos π= 1 ...

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Standard XII

Mathematics

Domain and Range of Basic Inverse Trigonometric Functions

If cos -1 x+c...

Question

If $c o s^{- 1} x + c o s^{- 1} y + c o s^{- 1} z = 3 π$ , then $x y + y z + z x =$

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Solution

The correct option is B 3
Given $c o s^{- 1} x + c o s^{- 1} y + c o s^{- 1} z = 3 π$
$∵ 0 \leq c o s^{- 1} x \leq π$
$∴ 0 \leq c o s^{- 1} y \leq π$ and $0 \leq c o s^{- 1} z \leq π$
Here $c o s^{- 1} x = c o s^{- 1} y = c o s^{- 1} z = π$
$\Rightarrow x = y = z = c o s π = - 1$
$∴ x y + y z + z x = (- 1) (- 1) + (- 1) (- 1) + (- 1) (- 1)$
$= 1 + 1 + 1 = 3$ .

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If cos−1x+cos−1y+cos−1z=3π, then xy+yz+zx=

The correct option is B 3Given cos−1x+cos−1y+cos−1z=3π ∵0≤cos−1x≤π ∴0≤cos−1y≤π and 0≤cos−1z≤π Here cos−1x=cos−1y=cos−1z=π ⇒x=y=z=cosπ=−1 ∴xy+yz+zx=(−1)(−1)+(−1)(−1)+(−1)(−1) =1+1+1=3.

If $c o s^{- 1} x + c o s^{- 1} y + c o s^{- 1} z = 3 π$ , then $x y + y z + z x =$