If A=\left(\begin{array}{cc}\cos \theta & - \sin \\\\theta \ \sin \\\\theta & \cos \theta)\end{array} and \theta=\frac{2 \pi}{7}, then A^{100}=A \times A \times . . .(100 times ) is equal to

Correct Answer is : (cos2θ−sin2θsin2θcos2θ)

\left(\begin{array}{cc}\cos 2 \theta & - \sin \\\2 \theta \ \sin \\\2 \theta & \cos 2 \theta)\end{array}

\left(\begin{array}{cc}\cos \theta & - \sin \\\\theta \ \sin \\\\theta & \cos \theta)\end{array}

\left(\begin{array}{cc}1 & 0 \ 0 & 1)\end{array}

\left(\begin{array}{cc}0 & -1 \ 1 & 0)\end{array}

WBJEE 2024 Math Paper

Question : 20 of 75

Marks: +1, -0

If A=(

cos‌θ	−sin‌θ
sin‌θ	cos‌θ

) and θ=‌

2π

, then A100=A×A×...(100 times ) is equal to

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cos‌2‌θ	−sin‌2θ
sin‌2θ	cos‌2‌θ

0	−1
1	0