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How to transform sin2x - cos2x into one trigonometry function?

Question:

How to move the graph of y = - (square root of 2) cos 2x to the graph of sin2x - cos2x?

Solution:

y = sin 2x - cos 2x
= - (cos 2x - sin 2x)
= - (cos 2x - sin 2x) (2/2)
= - (cos 2x - sin 2x) [(square root of 2)/2][square root of 2]
= - [cos 2x (square root of 2)/2 - sin 2x (square root of 2)/2] [square root of 2]
= - (square root of 2) [cos 2x cos (pi/4) - sin 2x sin (pi/4)]

Using the formula: cos (a + b) = cos a cos b - sin a sin b

y = sin 2x - cos 2x
= - (square root of 2) cos (2x + pi/4)
= - (square root of 2) cos 2(x + pi/8)

Therefore, move the graph of - (square root of 2) cos 2x left pi/8 units to get the graph of y = sin 2x - cos 2x. Watch the video for more details.