# If cos sin , sin cos 24 i A i é ù q q æ ö p = q = ê ú ç ÷ ë û q q è ø and 5 , a b A c d é ù = ê ú ë û where i = -1, then which one of the following is not true?

Question:

If $A=\left[\begin{array}{cc}\cos \theta & i \sin \theta \\ i \sin \theta & \cos \theta\end{array}\right],\left(\theta=\frac{\pi}{24}\right)$ and $A^{5}=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$, where $i=\sqrt{-1}$, then which one of the following is not true?

1. $0 \leq a^{2}+b^{2} \leq 1$

2. $a^{2}-d^{2}=0$

3. $a^{2}-c^{2}=1$

4. $a^{2}-b^{2}=\frac{1}{2}$

Correct Option: 4

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year Sep. 04, 2020 (I)

Solution:

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