Question

Спростіть вираз √2 cos (a + π/4)

Answer 1

Ответ:

$cos(a+ \frac{\pi}{4} )=cos(a)cos( \frac{\pi}{4} )+sin(a)sin( \frac{\pi}{4} )$

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Формула

$\sqrt{2} \cos(a + \frac{\pi}{4} )$

$\cos(a + \frac{\pi}{4} ) = \cos(a) ( \frac{1}{ \sqrt{2} } ) + \sin(a) ( \frac{1}{ \sqrt{2} } )$

$\sqrt{2} \cos(a + \frac{\pi}{4} ) = \sqrt{2} \cos(a) ( \frac{1}{ \sqrt{2} } ) + \sqrt{2} \sin(a) ( \frac{1}{ \sqrt{2} } )$

$\sqrt{2} \cos(a + \frac{\pi}{4} ) = \cos(a) + \sin(a)$