If A=[\table \cos \theta,\sin \theta;-\sin \theta,\cos \theta], then what is A^3 equal to ? [NDA I 2017]

Correct Answer is : [cos3θsin3θ−sin3θcos3θ]

[\table \cos 3\theta,\sin 3\theta;-\sin 3\theta,\cos 3\theta]

[\table \cos^3 \theta,\sin^3 \theta;-\sin^3 \theta,\cos^3 \theta]

[\table \cos 3\theta,-\sin 3\theta;\sin 3\theta,\cos 3\theta]

[\table \cos^3 \theta,-\sin^3 \theta;\sin^3 \theta,\cos^3 \theta]

UPSC NDA I 2017 Mathematics Solved Paper

Question : 51 of 120

Marks: +1, -0

If A=[

cos‌θ	sin‌θ
−sin‌θ	cos‌θ

], then what is A3 equal to ?

[NDA I 2017]

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cos‌2θ	sin‌2θ
−sin‌2θ	cos‌2θ

cos‌3θ	sin‌3θ
−sin‌3θ	cos‌3θ

cos3‌θ	sin3‌θ
−sin3‌θ	cos3‌θ

cos‌3θ	−sin‌3θ
sin‌3θ	cos‌3θ

cos3‌θ	−sin3‌θ
sin3‌θ	cos3‌θ