1)sin 45° * sin 15° 2) sin 105° – sin 75° 3) cos 75° - вопрос №44425381451521057537515 от макс3069 05.03.2020 06:18

Question

Математика: 1)sin 45° * sin 15° 2) sin 105° – sin 75° 3) cos 75° + cos 15° решить

макс3069 · Answer

1.  sin45*sin15=(√3-1)/4sin15=sin(45-30)=sin45*cos30-cos45*sin30=(√2/2)*(√3/2)-(√2/2)*(1/2)=√6/4-√2/4=(√6-√2)/4(√2/2)*(√6-√2)/4=(√2*√6-√2*√2)/8=(√12-√4)/8=(2√3-2)/8=2*(√3-1)/8=(√3-1)/42. sin105-sin75=0sin105=sin(60+45)=sin60*cos45+cos45*sin45=(√3/2)*(√2/2)+(√2/2)*(1/2)=(√2/2)*(√3/2+1/2)=2√*(√3+1)/8sin75=sin(45+30)=sin45*cos30+cos45*sin30=(√2/2)*(√3/2)+(√2/2)*(1/2)=(√2/2)*(√3/2+1/2)=(√2/2)*(√3+1)/2=√2*(√3+1)/8√2*(√3+1)/8-√2*(√3+1)/8=0и т.д....