1. In this question, you will be using the following trigonometric identities: = 1 cos² a + sin² a cos(a + 3) = cos a co

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1 In This Question You Will Be Using The Following Trigonometric Identities 1 Cos A Sin A Cos A 3 Cos A Co 1 (32.69 KiB) Viewed 48 times

1. In this question, you will be using the following trigonometric identities: = 1 cos² a + sin² a cos(a + 3) = cos a cos 8-sin a sin 3 = sin a cos ß + cos a sin 3 (2) sin(a + 3) (3) where a, BE R. You do not need to prove these identities. You may also use without proof the fact that the set QER is exactly the set of unit vectors in R². Now for any real number a, define [cos a Ra sin a (a) Prove that for all a, ß € R, Ra Ra = Ra+s (b) Using part (a), or otherwise, prove that R, is invertible and that R¹ = R-a, for all a E R. (c) Prove that for all a E R and all x, y € R², (Rax) (Ray) = x.y = sin a cos a