求证：sin^2(α+30°)+sin^2(α-30°)-sin^2α=定值
问题描述：
求证：sin^2(α+30°)+sin^2(α-30°)-sin^2α=定值
答
sin^2(α+30°)+sin^2(α-30°)-sin^2α=[1-cos(2α+60°)]/2+[1-cos(2α-60°)]/2-[1-cos(2α)]/2={1-[cos(2α+60°)+cos(2α-60°)]+cos2α}/2={1-2cos(2α)cos60°+cos(2α)}/2={1-cos(2α)+cos(2α)}/2=1/2