Mathematics · 2020
JEE Main · 4 September 2020, Shift 1 · Q54
If A = [cos θ, i sin θ; i sin θ, cos θ],(θ=(π)/24) and A^5= [a, b; c, d], where i=√ -1, then which one of the following is not true?
If $\displaystyle \mathrm{A}=\left[\begin{array}{cc}\cos \theta & i \sin \theta \\ i \sin \theta & \cos \theta\end{array}\right],\left(\theta=\frac{\pi}{24}\right)$ and $\displaystyle \mathrm{A}^5=\left[\begin{array}{ll}\mathrm{a} & \mathrm{b} \\ \mathrm{c} & \mathrm{d}\end{array}\right]$, where $\displaystyle i=\sqrt{-1}$, then which one of the following is not true ?
Official answer
(2)
$\displaystyle \mathrm{a}^2-\mathrm{b}^2=\frac{1}{2}$
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JEE Main 2020 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.