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Definition of a Determinant

If ϕ α ,β ...

Question

If $ϕ (α, β)$ $= ∣ ∣ ∣ ∣ \begin{matrix} cos α & - sin α & 1 sin α & cos α & 1 cos (α + β) & - sin (α + β) & 1 \end{matrix} ∣ ∣ ∣ ∣$ , then

A

f (300, 200) = f (400, 200)

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B

f (200, 400) = f (200, 600)

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C

f (100, 200) = f (200, 200)

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D

None of these

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Solution

The correct options are
A $f (300, 200) = f (400, 200)$
C $f (100, 200) = f (200, 200)$

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Similar questions

Q. The value of determinant

∣ ∣ ∣ ∣ \begin{matrix} cos α & - sin α & 1 sin α & cos α & 1 cos (α + β) & - sin (α + β) & 1 \end{matrix} ∣ ∣ ∣ ∣

\frac{2 sin α}{1 + cos α + sin α} = x

\frac{1 - cos α + sin α}{1 + sin α}

cos (α - β) = sin (α + β)

\frac{1}{1 - sin α} =

c o s α + c o s β + c o s γ = s i n α + s i n β + s i n γ = 0

c o s (β + γ) + c o s (γ + α) + c o s (α + β) = 0

s i n (β + γ) s i n (γ + α) + s i n (α + β) = 0

cos (α + β) = 0

sin (α - 2 β) =

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