If - - - - cos - - sin- 1 sin- cos- 1 cos - - - - sin - - - 1- then

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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

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

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

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

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none of these

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

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

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

α

f (α) = λ,

f (α)

α

cos (α - β) = sin (α + β)

\frac{1}{1 - sin α} =

x = sin α, y = sin β, z = sin (α + β)

cos (α + β)

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