百科知识

教育/科学

三角函数求值问题!!!(cos75°)^2+(cos15°)^+

2006-06-17 15:09:36若***
(cos75°)^2+(cos15°)^+cos75°+cos15°的值为?三角函数求值问题!!!(cos75°)^2+(cos15°)^+cos75°+cos15°的值为?：(cos75°)^2+(cos15°)^2+cos75°+c?

最佳回答

  • (cos75°)^2+(cos15°)^2+cos75°+cos15° =(cos75°)^2+(sin75°)^2+cos75°+sin75° =1+(√6-√2)/4+(√6+√2)/4 =1+√6/2
    2006-06-17 16:00:24
  •    (cos75°)^2+(cos15°)^2+cos75°+cos15° =cos(30°+45°)^2+[cos(45°-30°)]^2+cos(30°+45°)+cos(45°-30°) =(cos30°cos45°-sin30°sin45°)^2+[cos45°cos30°+sin45°sin30°]^2+[cos30°cos45°-sin30°sin45°]+[cos45°cos30°+sin45°sin30°] =[√3/2*√2/2-1/2*√2/2]^2+[√2/2*√2/2+√2/2*1/2]^2+[√3/2*√2/2-1/2*√2/2]+[√2/2*√3/2+√2/2*1/2] =(√6/2-√2/2)^2+[1+√2/2]^2+√6/2-√2/2+√6/2+√2/2 =(√6-√2)/2^2+(1+√2)/2^2+(√6+√6)/2 =(√6-√2)/2^2+(1+√2)/2^2+√6 。
      
    2006-06-17 22:02:59
  • 原式等于（1+cos150°)/2+(1+cos30°)/2+cos75°+sin75° =1+根号2倍的sin(75°+45°)=1+二分之根号6
    2006-06-17 15:44:55
    • 很赞哦！ (21)

    相关文章