Explain why #cos2y + sin2y = 1# equals to #sqrt2cos(2y-45^@) = 1# ?

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Answer 1 · 2017-06-19T04:09:21

Use trig identity:
#sin x + cos y = sqrt2.cos (x - pi/4)#
Replace in the equation x by 2y -->
#sin 2y + cos 2y = sqrt2cos (2y - pi/4) = 1#