QJEEM19Ma9238: JEE Main 2019 Mathematics - Class 12 JEEM19Ma9238 Solution: Let A = ( cos ⁡ α − sin ⁡ α sin ⁡ α cos ⁡ α ) , ( R) such that…

Question

Verified Solution • 2025–26 Session moderate

Let

A = (\begin{matrix} \cos α & - \sin α \\ \sin α & \cos α \end{matrix})

, (

\alpha

\in

R)
such that

A^{32} = (\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix})

then a value of

\alpha

is

Accepted Answer

From here sin 32

\alpha

= 1 and cos 32

\alpha

= 0

\therefore

32

\alpha

= 2n

\pi

+

{\pi \over 2}

\Rightarrow

\alpha

=

{\pi \over {64}} + {{n\pi } \over {16}}

Putting n = 0,

\alpha

=

{\pi \over {64}}

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