PYQ - Verify the following — task. Maths TNSB Mentoring, Class 10 Crash course.

If \(U =\)

(\begin{array}{l} \cos θ & 0 \\ 0 & \cos θ \end{array})

, \(V =\)

(\begin{array}{l} \sin θ & 0 \\ 0 & \sin θ \end{array})

then deduce that \(U^2 + V^2 = I\).

Answer:

Answer variants:

\(2 cos \theta\)

\cos^{2} θ

\(1\)

\(0\)

\(2 sin \theta\)

\sin^{2} θ

\(U^2 =\)

[\begin{array}{l} i & i \\ i & i \end{array}]

\(V^2 =\)

[\begin{array}{l} i & i \\ i & i \end{array}]

\(U^2 + V^2\) \(=\)

[\begin{array}{l} i & i \\ i & i \end{array}]

[By the trigonometric identity ]

\(U^2 + V^2 = I\)

Hence, proved.

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