Level 3
III. Complete the sentences
with the Present Perfect or
the Past Perfect.
10. It ... (to stop) raining by the
evening.
11. The boys ... (not to return)
from school yet.
12. My classmates ... (never to
do) such a difficult task.
13. You ... (to make) a decision
before our talk.
14. Mary ... (already to set) the
table for dinner.
15. His nephew ... (to move) to
a'new flat by the beginning
of September.​

Сначала формулы . затем формулы двойного угла sin2α=2sinαcosα cos2α=cos²α-sin²α=cos²α-(1-cos²α)=2cos²α-1⇒  2cos²α=1+cos2α cos2α=cos²α-sin²α=1-sin²α-sin²α=1-2sin²α⇒  2sin²α=1-cos2α а) сos75°cos105°=cos(90°-15°)·cos(90°+15°)== sin15°(-sin15°)=-sin²15°=-(1-cos30°)/2=(cos30°-1)/2= ((√3/2)-1)/2=0,25√3-0,5б) sin75°sin15°=°sin(90°-15°)sin15°=cos15° sin15°=sin30°/2=1/4=0,25в) sin105°cos15°=sin(180°-75°)cos15°=sin75°cos15°=sin(90°-15°)cos15°=cos15°cos15°=(1+cos30°)/2=(1+(√3/2))/2=0,5 +0,25√3 2 способ формулы cosα·cosβ=0,5cos(α-β)+0,5cos(α+β) sinα·sinβ=0,5cos(α-β)-0,5cos(α+β) sinα·cosβ=0,5sin(α+β)+0,5sin(α-β) а) сos75°cos105°=0,5cos(75°-105°)+0,5cos(75°+105°)=0,5cos(-30°)+0,5 cos180°==0,5· √3/2+0,5·(-1)=0,25√3-0,5б) sin75°sin15°=0,5cos(75°-15°)-0,5cos(75°+15° )=0,5cos60°-0,5 cos90°=0,5·0,5=0,25в) sin105°cos15°=0,5sin(105°+15°)+0,5sin(105°-15°)= =0,5sin120°+0,5sin90°==0,5 sin(180°-60°)+0,5·1=0,5 sin 60°+0,5=0,25√3+0,5

New year is my favorite holiday. On the eve of me always covers a strange feeling, as if something should happen joyful and magic. Everywhere the festive atmosphere, all are preparing for the holiday - choose a beautiful Christmas tree, buy a different fruits, sweets, prepared gifts for loved ones. Since childhood the New year is like a fairytale to me.

We start to prepare for the celebration in advance. Clean the house, decorate the Christmas tree, decorate the room with balloons, garlands, nice toys, festive lights, candles. I really like the new year and Christmas wreaths from branches of pine needles, bright ribbons and figures of angels. Before I saw this only in foreign films, and now this fashion has reached us.

My mother always cooks for the festive table, something небудничное. I try not to sleep the moment of arrival of the new year under the peal of bells. After the last hit on the street begins the fireworks that can last an hour! Each year we have the relatives come to visit and friends. We're having fun, hold various contests, dance, sing. It is always very interesting, but I usually early fall asleep. And in the morning I run right to the tree to see what I was given.

Especially well when the new year night stands frosty the snow weather. In all the houses the Windows are flashing colored lights. All celebrate and have fun. Apparently, due to the fact that New year is a common holiday, celebrate it's fun!