Sin 15 градусов+ tg 30 градусов*сos 15 градусов - вопрос №6295157153015 от lonelynightly 18.06.2021 17:46

Question

Математика: Sin 15 градусов+ tg 30 градусов*сos 15 градусов

lonelynightly · Answer

Sin15+tg30*cos15 = sin(45-30)+tg30*cos(45-30)=sin45*cos30-cos45*sin30+tg30*(cos45*cos30+sin45*sin30)=√2/2*√3/2-√2/2*1/2+√3/3*(√2/2*√3/2+√2/2*1/2)=(√6-√2)/4+√3/3((√6+√2)/4)=(√6-√2)/4+√3/12(√6+√2)=
=3(√6-√2)/12+√3/12(√6+√2)=(3√6-√2)/12+(√3*√6+√6)/12=(4√6+3√2-√2)/12=
=(4√6+2√2)/12=2(2√6+√2)/12=(2√6+√2)/6