Let \\theta=\\pi/5 and \A=[\table \cos\\theta,\sin\\theta;-\sin\\theta,\cos\\theta]. If \B=\A+{\A}^{4}, then {\det}({\B}): [6 Sep 2020 Shift 2]

Correct Answer is : lies in (1, 2)

JEE Mains 06-Sep-2020 Shift 2 Solved Paper

Section: Mathematics

Question : 61 of 75

Marks: +1, -0

Let θ=

and A=[

cos‌θ	sin‌θ
−sin‌θ	cos‌θ

]. If B=A+A4, then det(B):

[6 Sep 2020 Shift 2]

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cos‌2‌θ	sin‌2‌θ
−sin‌2‌θ	cos‌2‌θ

cos‌4‌θ	sin‌4‌θ
−sin‌4‌θ	cos‌4‌θ

(cos‌θ+cos‌4‌θ)	(sin‌θ+sin‌4‌θ)
−(sin‌θ+sin‌4‌θ)	(cos‌θ+cos‌4‌θ)