Question

求证(sina+sinb)^2+(cosa+cosb)^2=4cos^2[(a-b)/2]

Answer 1

证明：

左边=(sina)^2+(sinb)^2+2sinasinb+(cosa)^2+(cosb)^2+2cosacosb

=2+2(cosacosb+sinasinb)

=2+2cos(a-b)

=2+2{2cos^2[(a-b)/2]-1}

=4cos^2[(a-b)/2]

=右边

证毕