Question

证明 sin(25°)+sin(35°）= sin(85°)

Answer 1

sin(25°)+sin(35°)=sin(30°-5°)+sin(30°+5°)=sin(30°)cos(5°)-sin(5°)cos(30°)+sin(30°)cos(5°)+sin(5°)cos(30°)=2sin(30°)cos(5°)=cos(5°)=sin(85°)明白了吗？？

Answer 2

由三倍角公式
有 sin3a=3sina-4(sin^a)^3
cos3a=4(cosa)^2-3sina
tan3a=sin3a/cos3a=(3sina-4(sin^a)^3)/(4(cosa)^2-3sina) ****1
tan25°×tan35
tan(30-5)tan(30+5)
={(tan30-tan5)/(1+tan30tan5)}{(tan30+tan5)/(1-tan30tan5}
={1/3-(tan5)^2}{1-1/3(tan5)^2}
={1-3(tan5)^2}{3-1(tan5)^2}
=(4(cos5)^2-3)/(3-4(sin5)^2) ***2 (tan5=sin5/cos5
可以由右式 (sin5)^2+(cos5)^2=1整理
所以tan15°×tan25°×tan35
=****1 乘以****2 符号表示 约简
=tan5
所以tan15°×tan25°×tan35°×tan85°
=tan5*cot5=1

Answer 3

sin(25°)+sin(35°)= sin(30°-5°)+sin(30°+5°)=cos5°=sin85°。

Answer 4

sin25°＋sin35°=sin(30°－5°)＋sin(30°＋5°)=[sin30°cos5°－cos30°sin5°]＋[sin30°cos5°＋cos30°sin5°]=2sin30°cos5°=cos5°=sin85°

Answer 5

25=30-5 35=30+5 85=90-5 再利用和角化差公式