Question

Чему равно значение выражения:
1. tg п/3+ 2 ctg п/6
2. tg п/4+3 ctg 5п/6
3. 3 cos п/3+ 2 sin п/4
4. - sin п/2+ 2 ctg 3п/4

Answer 1

Нужно знать:

tg(π/3) = √3;          cos(π/3) = 1/2;          ctg(3π/4) = ctg(π - π/4) = -ctg(π/4) = -1;

ctg(π/6) = √3;        sin(π/2) = 1;               sin(π/4) = √2/2;

tg(π/4) = 1;              ctg(5π/6) = ctg(π - π/6) = -ctg(π/6) = -√3.

Поэтому:

1) tg(π/3) + 2ctg(π/6) = √3 + 2√3 = 3√3;

2) tg(π/4) + 3ctg(5π/6) = 1 + 3 · (-√3) = 1 - 3√3;

3) 3cos(π/3) + 2sin(π/4) = 3 · 1/2 + 2 · √2/2= 3/2 + √2= 1,5 + √2;

4) -sin(π/2) + 2ctg(3π/4) = -1 + 2 · (-1) = -1 - 2 = -3.