E-cos-sin-sin- cos-E-cos-sin-sin-cos- then find-E-E- -

Eα×Eβ=cosαsinα sinα nbsp;cosα×cosβsinβ sinβcosβ nbsp; nbsp;=cosαcosβ sinαsinβcosαsinβ+sinαcosβ sinαcosβ cosαsinβ sinαsinβ+cosαcosβ=cosα+βsinα+β sinα+βcosα ...

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Byju's Answer

Standard XII

Mathematics

Multiplication of Matrices

Eα=cosαsinα-s...

Question

$E_{α} = (\begin{matrix} cosα & sinα - sinα & cosα \end{matrix}] E_{β} = (\begin{matrix} cosβ & sinβ - sinβ & cosβ \end{matrix}] then find, Eα \times E_{β} ?$

E_{(α - β)}

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E_{(α + β)}

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E_{(α \times β)}

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E_{(α / β)}

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Solution

The correct option is B $E_{(α + β)}$
$E_{α} \times E_{β} = (\begin{matrix} cos (α) & sin (α) - sin (α) & cos (α) \end{matrix}] \times (\begin{matrix} cos (β) & sin (β) - sin (β) & cos (β) \end{matrix}] = (\begin{matrix} cos (α) cos (β) - sin (α) sin (β) & cos (α) sin (β) + sin (α) cos (β) - sin (α) cos (β) - cos (α) sin (β) & - sin (α) sin (β) + cos (α) cos (β) \end{matrix}] = (\begin{matrix} cos (α + β) & sin (α + β) - sin (α + β) & cos (α + β) \end{matrix}] = E_{(α + β)} \to option (b) is correct$

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Eα=(cosαsinα−sinα cosα]Eβ=(cosβsinβ−sinβcosβ] then find,Eα×Eβ ?

$E_{α} = (\begin{matrix} cosα & sinα - sinα & cosα \end{matrix}] E_{β} = (\begin{matrix} cosβ & sinβ - sinβ & cosβ \end{matrix}] then find, Eα \times E_{β} ?$