Question

Довести тотожність
sin( π\4 + 2) = cos (π\4 -2)

Answer 1

Ответ:

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

Answer 2

Ответ:

${}\qquad \qquad \qquad \boxed{\ sin\alpha =cos\Big(\dfrac{\pi}{2}-\alpha \Big)\ }\\\\\\\\sin\Big(\dfrac{\pi}{4}+2\Big)=cos\Big(\dfrac{\pi}{2}-\Big (\dfrac{\pi}{4}+2\Big)\Big)=cos\Big(\dfrac{\pi}{2}-\dfrac{\pi}{4}-2\Big)=cos\Big(\dfrac{\pi}{4}-2\Big)$