(i) If P(x)=cosxsinx-sinxcosx, then show that P(x) P(y) = P(x + y) = P – InterviewSolution

1.	(i) If P(x)=cosxsinx-sinxcosx, then show that P(x) P(y) = P(x + y) = P(y) P(x).(ii) If P=x000y000z and Q=a000b000c, prove that PQ=xa000yb000zc=QP
Answer» (i) If $P (x) = [\begin{matrix} \cos x & \sin x \\ - \sin x & \cos x \end{matrix}]$ , then show that P(x) P(y) = P(x + y) = P(y) P(x). (ii) If $P = [\begin{matrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{matrix}] and Q = [\begin{matrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{matrix}], prove that P Q = [\begin{matrix} x a & 0 & 0 \\ 0 & y b & 0 \\ 0 & 0 & z c \end{matrix}] = Q P$

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