Express cos^2 x in terms of cos2x. Hence, express f (x) = 6cos^2 x - 4sin 2x in the form R cos (2x + Y degrees) + p where R, y and p are constants. Find the maxium and minimum values of f (x) and sketch its graph in the domain - 180 < = x < = 360

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6 December, 20:45

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Savanah Vaughan · Answer 1

2cos^2 x = 1 + cos 2x

cos^2 x = 1/2 (1 + cos 2x)

f (x) = 6cos^2 x - 4 sin 2x = 6 (1/2 (1 + cos 2x) - 4 sin 2x = 3 + 3cos 2x - 4sin 2x