Question

Помогите решить ( с объяснением) Даю 20 баллов

Answer 1

sin(arctg(-1/4)-5π/2)=-sin(2π+π/2-arctg(-1/4)

=-cos(arctg(-1/4))
arctg(-1/4)=a€[-π/2;π/2]
tga=-1/4;а €[-π/2;0]
1+tg²a=1/cos²a
cos²a=1/(1+1/16)=16/17
cosa=4/√17
-cos(arctg(-1/4)=-4/√17=
-4√17/17