三角函数式的化简？ 三角函数式的化简
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\u5012\u6570\u5173\u7cfb: tan\u03b1 \u00b7cot\u03b1\uff1d1 sin\u03b1 \u00b7csc\u03b1\uff1d1 cos\u03b1 \u00b7sec\u03b1\uff1d1
\u5e73\u65b9\u5173\u7cfb\uff1a sin^2(\u03b1)\uff0bcos^2(\u03b1)\uff1d1 1\uff0btan^2(\u03b1)\uff1dsec^2(\u03b1) 1\uff0bcot^2(\u03b1)\uff1dcsc^2(\u03b1)
sin² \u03b1+cos² \u03b1=1 tan \u03b1 *cot \u03b1=1
\u9510\u89d2\u4e09\u89d2\u51fd\u6570\u516c\u5f0f
\u6b63\u5f26\uff1a sin \u03b1=\u2220\u03b1\u7684\u5bf9\u8fb9/\u2220\u03b1 \u7684\u659c\u8fb9 \u4f59\u5f26\uff1acos \u03b1=\u2220\u03b1\u7684\u90bb\u8fb9/\u2220\u03b1\u7684\u659c\u8fb9 \u6b63\u5207\uff1atan \u03b1=\u2220\u03b1\u7684\u5bf9\u8fb9/\u2220\u03b1\u7684\u90bb\u8fb9 \u4f59\u5207\uff1acot \u03b1=\u2220\u03b1\u7684\u90bb\u8fb9/\u2220\u03b1\u7684\u5bf9\u8fb9
\u4e8c\u500d\u89d2\u516c\u5f0f
\u6b63\u5f26 sin2A=2sinA\u00b7cosA \u4f59\u5f26 1.Cos2a=Cos^2(a)-Sin^2(a) =2Cos^2(a)-1 =1-2Sin^2(a) 2.Cos2a=1-2Sin^2(a) 3.Cos2a=2Cos^2(a)-1 \u6b63\u5207 tan2A=\uff082tanA\uff09/\uff081-tan^2(A)\uff09
\u534a\u89d2\u516c\u5f0f
tan(A/2)=(1-cosA)/sinA=sinA/(1+cosA); cot(A/2)=sinA/(1-cosA)=(1+cosA)/sinA. sin^2(a/2)=(1-cos(a))/2 cos^2(a/2)=(1+cos(a))/2 tan(a/2)=(1-cos(a))/sin(a)=sin(a)/(1+cos(a))
\u671b\u91c7\u7eb3\uff01
cost=1-2sin²(t/2)
所以，1-cost=2sin²(t/2)
所以，(1-cost)^4=[2sin²(t/2)]^4=16sin^8 (t/2)
已知三角函数关系公式cos2x＝1-2sin²x，所以2sin²x＝1-cos2x，把2x换成t，代入所给公式，得到
1-cost＝2sin²t/2，再进行乘方就可以了。
化简：
(1-cost)^4
={1-〔1-2(sint/2)^2〕}^4
={1-1+2(sint/2)^2}^4
={2(sint/2)^2}^4
=16(sint/2)^8
倒数关系:tanα·cotα＝1sinα·cscα＝1cosα·secα＝1
平方关系：sin^2(α)＋cos^2(α)＝11＋tan^2(α)＝sec^2(α)1＋cot^2(α)＝csc^2(α)
sin²；α+cos²；α=1tanα*cotα=1
锐角三角函数公式
正弦：sinα=∠α的对边/∠α的斜边余弦：cosα=∠α的邻边/∠α的斜边正切：tanα=∠α的对边/∠α的邻边余切：cotα=∠α的邻边/∠α的对边
二倍角公式
正弦sin2A=2sinA·cosA余弦1.Cos2a=Cos^2(a)-Sin^2(a)=2Cos^2(a)-1=1-2Sin^2(a)2.Cos2a=1-2Sin^2(a)3.Cos2a=2Cos^2(a)-1正切tan2A=（2tanA）/（1-tan^2(A)）
半角公式
tan(A/2)=(1-cosA)/sinA=sinA/(1+cosA)；cot(A/2)=sinA/(1-cosA)=(1+cosA)/sinA.sin^2(a/2)=(1-cos(a))/2cos^2(a/2)=(1+cos(a))/2tan(a/2)=(1-cos(a))/sin(a)=sin(a)/(1+cos(a))
望采纳！
因为 1-cost=2sin²t/2
所以 （1-cost）^4=16（sint/2）^8
原式成立。
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