如图,D是Rt△ABC斜边BC上一点,AB=AD,记∠CAD=α,∠ABC=β.(1)求证 sinα+sin^2β.(2)若AC=根号3DC,求β的值

问题描述:

如图,D是Rt△ABC斜边BC上一点,AB=AD,记∠CAD=α,∠ABC=β.(1)求证 sinα+sin^2β.(2)若AC=根号3DC,求β的值

因为AB=AD所以∠ABC=∠ADB=β∠ABC+∠ADB+∠DAB=180°即2β+∠DAB=180°-------1又因为是Rt△ABC所以∠CAD+∠DAB=90°即α+∠DAB=90 --------2设CD为a,则AC为√3a根据正弦定理a/sinα=√3a/sin2β推出sinα=sin2β...