Ответ:

[tex]cos(a+ \frac{\pi}{4} )=cos(a)cos( \frac{\pi}{4} )+sin(a)sin( \frac{\pi}{4} )[/tex]

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Формула

[tex] \sqrt{2} \cos(a + \frac{\pi}{4} ) [/tex]

[tex] \cos(a + \frac{\pi}{4} ) = \cos(a) ( \frac{1}{ \sqrt{2} } ) + \sin(a) ( \frac{1}{ \sqrt{2} } )[/tex]

[tex] \sqrt{2} \cos(a + \frac{\pi}{4} ) = \sqrt{2} \cos(a) ( \frac{1}{ \sqrt{2} } ) + \sqrt{2} \sin(a) ( \frac{1}{ \sqrt{2} } )[/tex]

[tex] \sqrt{2} \cos(a + \frac{\pi}{4} ) = \cos(a) + \sin(a) [/tex]