JEE Main20204 Sep 2020Morning ShiftMathematicsMatricesActual
If A = cos θ isin θ isin 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?
Options
- A0 ≤ a 2 + b 2 ≤ 1
- Ba 2 - d 2 = 0
- Ca 2 - c 2 = 1
- Da 2 - b 2 = 1 2
Correct answer
D. a 2 - b 2 = 1 2
Step-by-step solution
A 2 = cos θ        i sin θ i sin θ         cos θ cos θ        i sin θ i sin θ        cos θ = cos 2 θ − sin 2 θ        2 i sin θ cos θ 2 i sin θ cos θ            cos 2 θ − sin 2 θ = cos 2 θ      &#