Question

помогите плиз.Тригонометрия

Answer 1

$\frac{cos( - \frac{\pi}{12} ) - cos \frac{3\pi}{4} }{sin \frac{\pi}{12} - sin \frac{5\pi}{4} } = \frac{cos \frac{\pi}{12} - cos(\pi - \frac{\pi}{4} )}{sin \frac{\pi}{12} - sin(\pi + \frac{\pi}{4}) } = \frac{cos \frac{\pi}{12} + cos \frac{\pi}{4} }{sin \frac{\pi}{12} + sin \frac{\pi}{4} } = \frac{2cos( \frac{ \frac{\pi}{12} + \frac{\pi}{4} }{2})cos( \frac{ \frac{\pi}{12} - \frac{\pi}{4} }{2} ) }{2sin( \frac{ \frac{\pi}{12} + \frac{\pi}{4} }{2} )cos( \frac{ \frac{\pi}{12} - \frac{\pi}{4} }{2}) } = \frac{cos( \frac{\frac{4\pi}{12}}{2} )}{sin( \frac{ \frac{4\pi}{12} }{2} ) } = \frac{cos( \frac{\pi}{6} )}{sin( \frac{\pi}{6}) } = ctg \frac{\pi}{6} = \sqrt{3}$