If - - - are real numbers- then Delta - begin vmatrix 1 - cos beta-lalpha - coslgamma -lalpha-coslalpha -lgamma - cos beta -lgamma - 1 lend vmatrix

The correct option is D None of theseΔ = cos α amp; sin α amp; 0 cos β amp; sin β amp; 0 cos γ amp; sin γ amp; 0 × cos α amp; sin α amp; 0 ...

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Byju's Answer

Standard XII

Mathematics

Properties of Determinants

If α, β, γ ar...

Question

If $α, β, γ$ are real numbers, then $Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & c o s (β - α) & c o s (γ - α) c o s (α - β) & 1 & c o s (γ - β) c o s (α - γ) & c o s (β - γ) & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$

-1

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c o s α c o s β c o s γ

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c o s α + c o s β + c o s γ

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None of these

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Solution

The correct option is D None of these
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} c o s α & s i n α & 0 c o s β & s i n β & 0 c o s γ & s i n γ & 0 \end{matrix} ∣ ∣ ∣ ∣ \times ∣ ∣ ∣ ∣ \begin{matrix} c o s α & s i n α & 0 c o s β & s i n β & 0 c o s γ & s i n γ & 0 \end{matrix} ∣ ∣ ∣ ∣$

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Similar questions

Q. The value of

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & c o s (β - α) & c o s (γ - α) c o s (α - β) & 1 & c o s (γ - β) c o s (α - γ) & c o s (β - γ) & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

Q. If

α, β, γ, δ

are in

A . P .

and

2 \int 0 f (x) d x = - 4

, where

f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} x + α & x + β & x + α - γ x + β & x + γ & x - 1 x + γ & x + δ & x - β + δ \end{matrix} ∣ ∣ ∣ ∣ ∣

then common difference

d

is:

Q. If f(x) and g(x) are functions such that f(x + y) = f(x).g(y) + g(x).f(y), then

∣ ∣ ∣ ∣ ∣ \begin{matrix} f (α) & g (α) & f (α + θ) f (β) & g (β) & f (β + θ) f (γ) & g (γ) & f (γ + θ) \end{matrix} ∣ ∣ ∣ ∣ ∣

is independent of

Evaluate $∣ ∣ ∣ ∣ \begin{matrix} c o s α c o s β & c o s α s i n β & - s i n α - s i n β & c o s β & 0 s i n α c o s β & s i n α s i n β & c o s α \end{matrix} ∣ ∣ ∣ ∣$

If the value of determinant $∣ ∣ ∣ ∣ \begin{matrix} x + 1 & α & β α & x + β & 1 β & 1 & x + α \end{matrix} ∣ ∣ ∣ ∣$ is equal to -8, then the value of x, is (where $α, β$ are non real cube roots of unity)

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If α,β,γ are real numbers, then Δ=∣∣ ∣ ∣∣1cos(β−α)cos(γ−α)cos(α−β)1cos(γ−β)cos(α−γ)cos(β−γ)1∣∣ ∣ ∣∣

The correct option is D None of theseΔ=∣∣ ∣∣cosαsinα0cosβsinβ0cosγsinγ0∣∣ ∣∣×∣∣ ∣∣cosαsinα0cosβsinβ0cosγsinγ0∣∣ ∣∣

If $α, β, γ$ are real numbers, then $Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & c o s (β - α) & c o s (γ - α) c o s (α - β) & 1 & c o s (γ - β) c o s (α - γ) & c o s (β - γ) & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$