Question

20.18. Помогите пажалуста дам 30 балл​

Answer 1

Ответ:

1.

$\frac{ {( - \sin(30°) - \cos(30°) )}^{2} }{3 \cos(45°) \sin(45°) - 6tg(30°)ctg(60°)} = \\ = \frac{ {( \frac{1}{2}) }^{2} + 2 \times \frac{1}{2} \times \frac{ \sqrt{3} }{2} + {( \frac{ \sqrt{3} }{2}) }^{2} }{3 \times \frac{ \sqrt{2} }{2} \times \frac{ \sqrt{2} }{2} - 6 \times \frac{ \sqrt{3} }{3} \times \frac{ \sqrt{3} }{3} } = \\ = \frac{ \frac{1}{4} + \frac{ \sqrt{3} }{2} + \frac{3}{4} }{ \frac{3}{2} - 2 } = (1 + \frac{ \sqrt{3} }{2} ) \times ( - 2 )= \\ = -2- \sqrt{3}$

2.

$\frac{2 {tg}^{2}( \frac{\pi}{3} ) \cos(\pi) - 1}{ \sin( \frac{\pi}{2} ) \cos( \frac{\pi}{3} )tg( \frac{\pi}{4} ) } = \\ = \frac{2 \times {( \sqrt{3}) }^{2} \times ( - 1) - 1}{1 \times \frac{1}{2} \times 1} = \\ = \frac{ - 6 - 1}{ \frac{1}{2} } = - 7 \times 2 = - 14$

3.

$\frac{ \sqrt{ {( \cos(60°) - \sin(60°)) }^{2} } }{ \sin(30°) \times (1 - tg(60°)) } = \\ = \frac{ | \cos(60°) - \sin(60°) | }{ \frac{1}{2} \times (1 - \sqrt{3} )} = \\ = | \frac{1}{2} - \frac{ \sqrt{3} }{2} | \times \frac{2}{1 - \sqrt{3} } = (\frac{ \sqrt{3} }{2} - \frac{1}{2}) \times \frac{2}{1 - \sqrt{3} } = \\ = - \frac{1}{2} (1 - \sqrt{3} ) \times \frac{2}{1 - \sqrt{3} } = - 1$

4.

$\frac{ \sqrt{ {(tg \frac{\pi}{6} - tg \frac{\pi}{3}) }^{2} } }{ {(ctg \frac{\pi}{6} - ctg \frac{\pi}{3} ) }^{2} } = \frac{ | \frac{ \sqrt{3} }{3} - \sqrt{3} | }{ {( \sqrt{3} - \frac{ \sqrt{3} }{3}) }^{2} } \\ = \frac{ \sqrt{3} - \frac{ \sqrt{3} }{3} }{ {( \sqrt{3} - \frac{ \sqrt{3} }{3}) }^{2} } = \frac{1}{ \sqrt{3} - \frac{ \sqrt{3} }{3} } = \frac{3}{3 \sqrt{3} - \sqrt{3} } = \\ = \frac{ 3 }{2 \sqrt{3} } = \frac{ \sqrt{3} }{2}$