Question

高中解三角形习题已知△ABC中 角A=60度求(cosB)^2+(cosC)^2的取值范围

Answer 1

A=60度,则B+C=120度,

(cosB)^2+(cosC)^2

=(1+cos2B)/2+(1+cos2C)/2

=(cos2B+cos2C)/2+1

=1/2*[cos2B+cos(240-2B)]+1

=1/2*[cos2B-1/2*cos2B-√3/2*sin2B]+1

=1/2*[1/2*cos2B-√3/2*sin2B]+1

=1/2*cos(2B+60)+1

由 0