Question

Найдите sina+2cosa если tga/2=-2

Answer 1

tga=2tg(a/2)/(1-tg²(a/2))=2*(-2)/(1-4)=-4/-3=4/3
cos²a=1;(1+tg²a)=1:(1+16/9)=1:25/9=9/25⇒cosa=-3/5 или cosa=3/5
1)cosa=-3/5⇒sina=√1-9/25=√16/25=4/5
sina+2cosa=4/5-2*3/5=4/5-6/5=-2/5
2)cosa=3/5⇒sina=-√1-9/25=-√16/25=-4/5
sina+2cosa=-4/5+2*3/5=-4/5+6/5=2/5