Question

在三角形ABC中,A`B`C是其三个内角,且f(A)=2sin(∏/2+A/2)+cos(2∏-A/2)

Answer 1

f(A)=2sin(∏/2+A/2)+cos(2∏-A/2)+cos^2(3∏/2+A/2)-sin^2(A/2-∏/2).

=2cosA/2+cosA/2+sin²A/2-cos²A/2

=3cosA/2+1-2cos²A/2

f(π/3)=3cosπ/6+1-2cos²π/6

=3√3/2+1-2*3/4

=(3√3-1)/2

f(A) =-2cos²A/2+3cosA/2+1

=-2(cosA/2-3/4)²+17/8