Question

памагите пожалста ссрочнономера 20,12 20,13

Answer 1

Ответ:

2012

1 .

$\sin( \frac{\pi}{6} ) \times (tg( \frac{\pi}{4}) + \cos( \frac{\pi}{3} ) ) = \\ = \frac{1}{2} \times ( 1 + \frac{1}{2} ) = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} = 0.75$

2.

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

3.

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

2013

1.

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

2.

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

3.

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