Math, asked by chiragdhoot03, 1 year ago

plz solve this question

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Answers

Answered by bhaskarreddy12
1
option 4 is the answer
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Answered by hasnainrabby
1

Answer: (4)  

                    \left[\begin{array}{ccc}cos2\alpha &sin2\alpha \\-sin2\alpha &cos2\alpha \\\end{array}\right]

Step-by-step explanation:

Let A = \left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]

∴ A⁻¹ = 1/|A| \left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]          [|A| = adj.Matrix.

we know,

|A| = ad - bc

Now in our math,

\left[\begin{array}{ccc}cos2\alpha &-sin2\alpha \\sin2\alpha &cos2\alpha \\\end{array}\right] = A

|A| = cos2\alpha cos2\alpha - (-sin2\alpha sin2\alpha )

    = cos^{2}2\alpha  + sin^{2}2\alpha

    = 1     [sin^{2}\alpha + cos^{2}\alpha = 1   ]

so,

A⁻¹ = 1/1  \left[\begin{array}{ccc}cos2\alpha &sin2\alpha \\-sin2\alpha &cos2\alpha \\\end{array}\right]

= \left[\begin{array}{ccc}cos2\alpha &sin2\alpha \\-sin2\alpha &cos2\alpha \\\end{array}\right]

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