If A=(\table \cos\alpha,\sin\alpha;-\sin\alpha,\cos\alpha), then A^{10} is equal to

Correct Answer is : (cos10αsin10α−sin10αcos10α)

(\table \cos^{10}\alpha,\sin^{10}\alpha;-\sin^{10}\alpha,\cos^{10}\alpha)

(\table \cos^{10}\alpha,-\sin^{10}\alpha;\sin^{10}\alpha,\cos^{10}\alpha)

(\table \cos^{10}\alpha,\sin^{10}\alpha;-\sin^{10}\alpha,-\cos^{10}\alpha)

(\table cos10\alpha,sin10\alpha;-sin10\alpha,\cos^10\alpha)

(\table cos10\alpha,-sin10\alpha;-sin10\alpha,-\cos^10\alpha)

KEAM 2011 Math Paper

Question : 104 of 120

Marks: +1, -0

If A=(

cosα	sinα
−sinα	cosα

), then A10 is equal to

(
cos10α sin10α
−sin10α cos10α
)
(
cos10α −sin10α
sin10α cos10α
)
(
cos10α sin10α
−sin10α −cos10α
)
(
cos10α sin10α
−sin10α cos10α
)
(
cos10α −sin10α
−sin10α −cos10α
)

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cos‌α	sin‌α
−sin‌α	cos‌α

cos‌α	sin‌α
−sin‌α	cos‌α

cos‌α	sin‌α
−sin‌α	cos‌α

cos2α−sin2α	2‌sin‌α‌cos‌α
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−sin‌2‌α	cos‌2‌α

cos10α	sin10α
−sin10α	cos10α

cos10α	−sin10α
sin10α	cos10α

cos10α	sin10α
−sin10α	−cos10α

cos10α	sin10α
−sin10α	cos10α