Question

найти значение выражения (5cos 2a +3)/(3-8cos²a)
если tg a= -√5

Answer 1

(5cos2α+3)/(3-8cos²α)=(5(2cos²α-1)+3)/(3-8cos²α)=(10cos²α-5+3)/(3-8cos²α)=
=(10cos²α-2)/(3-8cos²α)
1+tg²α=1/cos²α
1+(-√5)²=1+5=6
1/cos²α=6, =>cos²α=1/6
(10*(1/6)-2)/(3-8*(1/6))=(10/6-2)/(3-8/6)=(10/6-12/6)/(18/6-8/6)=
=(-2/6)/(10/6)=-1/5=-0.2