Question

упростите выражение $sqrt{2} sin( frac{ pi }{4}+ alpha )-cos alpha$

Answer 1

$sqrt2sin(frac{pi}{4}+ alpha )-cos alpha =sqrt2(sinfrac{pi}{4}cos alpha +cosfrac{pi}{4}sin alpha) -cos alpha =\\=sqrt2(frac{sqrt2}{2}cos alpha +frac{sqrt2}{2}sin alpha )-cos alpha =cos alpha +sin alpha -cos alpha =sin alpha$