sin²1°+sin²2°+.+sin²89°+sin²90°=?
问题描述:
sin²1°+sin²2°+.+sin²89°+sin²90°=?
答
sin²a+cos²a=1sina=cos(90-a)则sin89=cos1,sin88=cos2……所以原式=(sin²+1cos²1)+……+(sin²44+cos²44)+sin²45+sin²90=1×44+1/2+1=91/2