Question

在△ABC中，角A、B、C所对的边分别是a、b、c且cosA=4/5

求sin^2(B+C)/2+cos2A的值
求详解

Answer 1

B+C=π-A
sin^2(B+C)/2+cos2A
=sin^2[π/2-A/2]+cos2A
=cos^2(A/2)+cos2A
=(1+cosA)/2+2cos^2A-1 cosA=4/5
=(1+4/5)/2+32/25-1
=9/10+7/25
=59/50