The value of the determinant ax - a-x2 ax - a-x2 1 bx - b-x2 bx - b-x2 1 cx - c-x2 cx - c-x2 1 is

The correct option is D 0 Given determinant is = #160;(a^x + a^ x)^2 amp; (a^x a^ x)^2 #160; amp; 1 (b^x + b^ x)^2 #160; amp; (b^x ...

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Definition of a Determinant

The value of ...

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The value of the determinant $∣ ∣ ∣ ∣ ∣ \begin{matrix} (a^{x} + a^{- x})^{2} & (a^{x} - a^{- x})^{2} & 1 (b^{x} + b^{- x})^{2} & (b^{x} - b^{- x})^{2} & 1 (c^{x} + c^{- x})^{2} & (c^{x} - c^{- x})^{2} & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$ is

0

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2 a b c

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a^{2} b^{2} c^{2}

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None of these

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∣ ∣ ∣ ∣ ∣ \begin{matrix} {(a^{x} + a^{- x})}^{2} & {(a^{x} - a^{- x})}^{2} & 1 {(b^{x} + b^{- x})}^{2} & {(b^{x} - b^{- x})}^{2} & 1 {(c^{x} + c^{- x})}^{2} & {(c^{x} - c^{- x})}^{2} & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

a, b, c > 0

x, y, z

\in

∣ ∣ ∣ ∣ ∣ \begin{matrix} (a^{x} + a^{- x})^{2} & (a^{x} - a^{- x})^{2} & 1 (b^{y} + b^{- y})^{2} & (b^{y} - b^{- y})^{2} & 1 (c^{z} + c^{- z})^{2} & (c^{z} - c^{- z})^{2} & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

a, h, 0 > 0

x, y, z ϵ R

∣ ∣ ∣ ∣ ∣ \begin{matrix} {(a^{x} + a^{- x})}^{2} & {(a^{x} - a^{- x})}^{2} & 1 {(b^{y} + b^{- y})}^{2} & {(b^{y} - b^{- y})}^{2} & 1 {(c^{z} + c^{- z})}^{2} & {(c^{z} + c^{- z})}^{2} & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

a, b, c > 0

x, y, z ϵ R

∣ ∣ ∣ ∣ ∣ \begin{matrix} (a^{x} + a^{- x})^{2} & (a^{x} - a^{- x})^{2} & 1 (b^{y} + b^{- y})^{2} & (b^{y} - b^{- y})^{2} & 1 (c^{z} + c^{- z})^{2} & (c^{z} - c^{- z})^{2} & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

a, b, c > 0

x, y, z \in R

∣ ∣ ∣ ∣ ∣ \begin{matrix} {(a^{x} + a^{- x})}^{2} & {(a^{x} - a^{- x})}^{2} & 1 {(b^{y} + b^{- y})}^{2} & {(b^{y} - b^{- y})}^{2} & 1 {(c^{z} + c^{- z})}^{2} & {(c^{z} - c^{- z})}^{2} & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

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