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Is there a way to show this using linear algebra? I have expanded it and shown through the multiplication and trig identities that it is true but it required a whole page of work, I am thinking there may be an easier way?
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since |A| = 1
REMEMber that Cos^2 + sin^2 = 1 by trig identities
@rock_mit182 a more useful identity in this case is (cos(x))^2-(sin(x))^2 = cos(2x) but my professor has pointed out that I am doing great on quizzes and tests but I am using "old" methods and need to depend on properties of linear algebra to simplify matters. So in this problem I have come to the solution, but through actually multiplying them out, and using trig identities. My question is not how to obtain an answer, but rather is there a way to do this VIA linear algebra properties that does not require me to expand the matrices using multiplication and using trig identities to verify the truth of the statement?