8cos105sin165 Вычислите. Created by Elchin9. algebra-ru

8cos105sin165 Вычислите...

flaymak $8cos105\cdot sin165=8cos(90+15)\cdot sin(90+75)=8(-sin15)\cdot cos75=\\\\=-8\cdot \frac{1}{2}(sin(15+75)+sin(15-75))=-4\cdot (sin90-sin60)=\\\\=-4\cdot (1-\frac{\sqrt3}{2})=2\sqrt3-4$

$sin \alpha \cdot cos \beta =\frac{1}{2}\cdot (sin( \alpha + \beta )+sin( \alpha - \beta ))$

1 votes Thanks 0

NNNLLL54

Verified answer

8 * cos 105 * sin 165 = 8 * cos(pi/2+15) * sin (pi - 15) = 8 * cos pi/2 * cos 15 - sin pi/2 * sin 15 * sin pi * cos 15 - cos pi * sin 15 = 8*0*cos15 - 1 * sin 15 * 0 * cos 15 + 1 * sin 15 = sin 15
sin 15 = sin (45-30) = sin 45 * cos 30 - cos 45 sin 30 = корень из 2/2 * корень из 3 / 2 - корень из 2 / 2 * 1/2 = $(\sqrt{6})/4 - (\sqrt{2}) /4 = [tex] \frac{ \sqrt{2}*( \sqrt{3} - 1) }{4}$

0 votes Thanks 0

Answers & Comments

Verified answer

peresekayas s osyami koordinat pryamaya axby10 pri agt0 bgt0 obrazuet treu

4 opredelite cosb

uprosti sin2p1cos2p 1

117 reshite

376 reshite pozhalujsta

reshite zabyl kak sdelat

4...

sin4a ctg2a uprostite

sina cosp vychislie sin2a

najdite procentnoe soderzhanie rastvora soli poluchennogo pri smeshivanii 15 litro

рекомендуемые вопросы

Helpful Links

Helpful Social