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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

Note: pi/6 = 30o, so cos (pi/6) = half of square root of 3 and sin (pi/6) = 1/2. So, y = (half of square root of 3) × sin 2x + (1/2) cos 2x - 1/2 - (1/2) cos 2x = -1/2 + half of square root of 3) sin 2x = -0.5 + 0.866 sin 2x. Look the video for the graph.