Question: Problem 2. Using the identities sin(x) = sin(x -2x) and sin(x) = sin(-x - 7), show why the following statements are true. 1. arcsin(sin(x) )

Problem 2. Using the identities sin(x) = sin(x -2x) and sin(x) = sin(-x - 7), show why the following statements are true. 1. arcsin(sin(x) ) = x - 2x for all x E [37 /2, 5x/2]. 2. arcsin (sin(x)) = -x - " for all re [-3x/2, -7/2]. Problem 3. Prove the following identities. 1. tan(arcsin(x)) = V1 - x2 2. sin(arctan(x) ) = V1+ x2

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