Question

Упростите: сos2 α +(1- sin2 α)

Answer 1

$cos2a+(1-sin2a)=\\\\=(cos^2a-sin^2a)+(sin^2a+cos^2a)-2sina\, cosa=\\\\=2cos^2a-2sina\, cosa=2cosa\cdot (cosa-sina)=\\\\=2cosa\cdot (cosa-cos(\frac{\pi }{2}-a))=-2cosa\cdot 2sin\frac{\pi }{4}\cdot sin(a-\frac{\pi }{4})=\\\\=2\sqrt2\cdot cosa\cdot sin(\frac{\pi }{4}-a)$

Answer 2

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