Question

Вычислите значение выражения: ​

Answer 1

1.

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

2.

$ctg \frac{\pi}{6} \times ( \sin( \frac{\pi}{3} ) - 3 \cos( \frac{\pi}{3} ) ) = \\ = \sqrt{3} \times ( \frac{ \sqrt{3} }{2} - 3 \times \frac{1}{2} ) = \\ = \sqrt{3} \times \frac{ \sqrt{3} - 3}{2} = \frac{3 - 3 \sqrt{3} }{2}$

3.

$\cos( \frac{\pi}{4} ) \times (2ctg \frac{\pi}{4} - 3 \sin( \frac{\pi}{6} ) ) = \\ = \frac{ \sqrt{2} }{2} \times (2 \times 1 - \frac{3}{2} ) = \\ = \frac{ \sqrt{2} }{2} \times \frac{1}{2} = \frac{ \sqrt{2} }{4}$