Question

Люди вычислите: а)корень из 3 sin60° +cos60°*sin30°-tg45°*ctg135°+ctg90° б)cos п/6-корень из двух sin п/4+ корень из 3 tg п/3

Answer 1

а) $\sqrt{3}sun60`+cos60`*sin30`-tg45`*ctg135`+ctg90`$

ctg135 = ctg(90+45) = -tg45

sin30 = 1/2

$sin60` = \sqrt{3}/2$ 

cos60 = 1/2

tg45 = 1

ctg90 = 0

$\sqrt{3} + \sqrt{3}/2 + 1/2 * 1/2 + 1^2 + 0 = \frac{3}{2}+\frac{1}{4}+1 = \frac{11}{4}$ 

б) $cos(\pi/6) - \sqrt{2}sin(\pi/4) + \sqrt{3}tg(\pi/3)$

$cos(\pi/6) = \sqrt{3}/2$ 

$sin(\pi/4) = \sqrt{2}/2$ 

$tg(\pi/3) = \sqrt{3}$

$\sqrt{3}/2 - \sqrt{2} * \sqrt{2}/2 + \sqrt{3}*\sqrt{3} = \sqrt{3}/2 - 1+3 = \sqrt{3}/2 + 2$