<span>1. cos(-210) = cos(210) = cos (180 + 30) = cos(π + π/3) - дальше по формуле приведения.</span>
<span><span>2. tg4П/3 = tg(π + π/3) - дальше по формуле приведения.</span></span>
<span><span><span>3. 2sinП/2-tgП/3 - табличные значения, подставляете и считаете.</span></span></span>
<span><span><span><span>4. sin 2x=1 => 2x = π/2 +πn => x = π/4 + πn/2</span></span></span></span>
<span><span><span><span><span>5. cos x*cos 2x+sin x*sin 2x=0</span></span></span></span></span>
Перепишем:
cos 2x*cos x+sin 2x*sin x=0
cos 2x*cos x = (cos(2x-x)+cos(2x+x))/2 = (cosx + cos3x)/2
sin 2x*sin x = (cos(2x-x)-cos(2x+x))/2 = (cosx - cos3x)/2
cos 2x*cos x+sin 2x*sin x=(cosx + cos3x)/2+(cosx - cos3x)/2
(cosx + cos3x)/2+(cosx - cos3x)/2=0
cosx + cos3x + cosx - cos3x = 0
2cosx = 0
x = π/2 + πn