Question

Формулы суммы и разницы
cos π/8-sin π/8
sin a - cos (a-60°)
sin 25° + cos 55°
cos 22°-sin 66°

Answer 1

$1) \cos( \frac{\pi}{8} ) - \sin( \frac{\pi}{8} ) \\ \\ \sqrt{ \frac{1 + \cos( \frac{\pi}{4} ) }{2} } - \sqrt{ \frac{1 - \cos( \frac{\pi}{4} ) }{2} } \\ \\ \sqrt{ \frac{1 + \frac{ \sqrt{2} }{2} }{2} } - \sqrt{ \frac{1 - \frac{ \sqrt{2} }{2} }{2} } \\ \\ \frac{ \sqrt{2 + \sqrt{2} } }{2} - \frac{ \sqrt{2 - \sqrt{2} } }{2} \\ \\ \frac{ \sqrt{2 + \sqrt{2} } - \sqrt{2 - \sqrt{2} } }{2} \\ \\ 2) \sin(a) - \cos(a - 60) \\ \\ \sin(a) - ( \cos(a) \times \cos(60) + \sin(a) \times \sin(60) ) \\ \\ \sin(a) - ( \frac{ \cos(a) }{2} + \frac{ \sqrt{3 } \times \sin(a) }{2} \\ \\ \sin(a) - \frac{ \cos(a) + \sqrt{3} \times \sin(a) }{2}$

$3) \sin(25) + \cos(55) \\ \\ \sin(25) + \cos(90 - 35) \\ \\ \sin(25) + \sin(35) \\ \\ 2 \sin(30) \times \cos( - 5) = \cos(5) \\ \\ \\ 4) \cos(22) - \sin(66) = 0.0136$

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