Questions

# If

## Unlock the full solution & master the concept.

Get a detailed solution and exclusive access to our masterclass to ensure you never miss a concept
By Expert Faculty of Sri Chaitanya
a
$A$
b
${A}^{2}$
c
${A}^{3}$
d
${A}^{4}$

Check Your Performance Today with our Free Mock Tests used by Toppers!

detailed solution

Correct option is D

$Let\text{\hspace{0.17em}\hspace{0.17em}}\theta =\frac{2\pi }{33}⇒A=\left[\begin{array}{cc}\mathrm{cos}\theta & \mathrm{sin}\theta \\ -\mathrm{sin}\theta & \mathrm{cos}\theta \end{array}\right]$

$⇒{A}^{2017}=\left[\begin{array}{cc}\mathrm{cos}2017\text{\hspace{0.17em}}\theta & \mathrm{sin}2017\text{\hspace{0.17em}}\theta \\ -\mathrm{sin}2017\text{\hspace{0.17em}}\theta & \mathrm{cos}2017\text{\hspace{0.17em}}\theta \end{array}\right]$

$2017\text{\hspace{0.17em}}\theta =\left(2017\right)\frac{2\pi }{33}=122\pi +\frac{8\pi }{33}⇒\mathrm{cos}\left(2017\text{\hspace{0.17em}}\theta \right)=\mathrm{cos}4\text{\hspace{0.17em}}\theta ;$

$\mathrm{sin}\left(2017\theta \right)=\mathrm{sin}4\theta$

Get your all doubts cleared from
Sri Chaitanya experts

+91