求证sin^2α+sin^2β-sin^2αsin^2β+cos^2cos^2β=1
问题描述：
求证sin^2α+sin^2β-sin^2αsin^2β+cos^2cos^2β=1
答
左边=sin^2α(1-sin^2β)+sin^2β+cos^2cos^2β
=sin^2αcos^2β+cos^2cos^2β+sin^2β
=(sin^2α+cos^2α)cos^2β+sin^2β
=cos^2β+sin^2β
=1=右边
命题得证