Given the function f (x) = cosx cos (x + pi / 2), X belongs to R. (1) find the maximum of F (x); (2) if f (a) = 3 / 4, find the value of sin2a

F (x) = cosx + SiNx = √ 2 (√ 2 / 2 * SiNx + √ 2 / 2cosx) = √ 2 (sinxcos π / 4 + cosxsin π / 4) = √ 2Sin (x + π / 4) so: the maximum value of F (x) = 2F (a) = cosa + Sina = 3 / 4sin & # 178; a + cos & # 178; a + 2sinacosx = 9 / 161 + sin2a = 9 / 16, so: sin2a = - 7 / 16

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