Draw graph of y = sin (2x + pi/6) - cos² x

Using the trigonometry sum of two angles formula, sin (a + b) = sin a cos b + cos a sin b and formula, cos² a = [1 + cos 2a]/2, then

y = sin (2x + pi/6) - cos² x

= sin (2x) cos (pi/6) + cos (2x) sin (pi/6) - [1 + cos 2x]/2

= [Sqrt (3)/2] sin (2x) + (1/2) cos (2x) - 1/2 - (1/2) cos (2x)

= [Sqrt (3)/2] sin (2x) - 1/2

= -0.5 + 0.866 sin 2x

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