I'd like to ask how to get to the final line of equation 6.22, I wonder about the cos and sin functions in particular. (page 257 Nielsen-Chuang) 
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1$\begingroup$ See Exercises 4.2 and 4.4 of N&C. If you are stuck, see my solutions manual, but try to do as much yourself as possible. If you find this exercise quite confusing it may benefit you to revisit Ch 2. $\endgroup$– JacobCommented Apr 21, 2023 at 20:11
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$\begingroup$ If this satisfies you, I might suggest closing your question. As you can see it is not really a question about search as much as qubit operations. $\endgroup$– JacobCommented Apr 21, 2023 at 20:16
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