高一数学 三角比诱导公式的题

\u9ad8\u4e00\u6570\u5b66\u9898\uff0c\u5173\u4e8e\u4e09\u89d2\u6bd4\u8bf1\u5bfc\u516c\u5f0f\uff0c\u8c22\u8c22\uff01\uff01\uff01\uff01\uff01\uff01\uff01\uff01\uff01\uff01\uff01\uff01\uff01\uff01

1\u3001
\u539f\u5f0f=(1-cos^4a/sin^4a)*sin²a+cos²a/sin²a
=sin²a-cos^4a/sin²a+cos²a/sin²a
=sin²a+(cos²a-cos^4a)/sin²a
=sin²a-cos²a(1-cos²a)/sin²a
=sin²a-cos²asin²a/sin²a
=sin²a-cos²a
=-cos2a


2\u3001
sin\u03b8-cos\u03b8=1/2
\u5e73\u65b9
sin²\u03b8-2sin\u03b8cos\u03b8+cos²\u03b8=1/4
1-2sin\u03b8cos\u03b8=1/4
sin\u03b8cos\u03b8=3/8

\u539f\u5f0f=(sin\u03b8-cos\u03b8)(sin²\u03b8+sin\u03b8cos\u03b8+cos²\u03b8)
=1/2*(1+3/8)
=-11/16

\u56e0\u4e3atanX=y/x \u5c31\u662f\u53d6\u67d0\u4e00\u70b9\u7684\u5750\u6807\u4e3a\uff08x,y\uff09,\u8fd9\u4e2a\u77e5\u9053\u5427\uff1f

\u7136\u540ey/x=\u6839\u53f73\uff0cy=\u6839\u53f73\uff0cx=1
\u753b\u4e00\u4e2a\u4e09\u89d2\u5f62\uff0c\u6216\u8005\u753b\u4e2a\u5750\u6807\u770b\u4e09\u89d2\u51fd\u6570\u7ebf\u3002
\u53c8\u56e0\u4e3ax\u2208[ 0\uff0c2\u220f\uff09
\u6240\u4ee5\u2460x=30\u00b0\uff0c
tanX= -tan(\u220f-x) \u6240\u4ee5\u2461x=150\u00b0
tanx=tan(\u220f+x) \u6240\u4ee5\u2462x=210\u00b0
tan(2\u220f-x)=tanx \u6240\u4ee5\u2463x=330\u00b0

\u7efc\u4e0a\uff0cx=30\u00b0\uff0c150\u00b0\uff0c210\u00b0\uff0c330\u00b0

\u5e0c\u671b\u5bf9\u4f60\u6709\u6240\u5e2e\u52a9\u54c8\uff01\u6211\u8981\u5206\u5206\uff01\u8c22\u8c22\uff01

答案 ： sina

tana(cosa-sina)+(sina+tana)/(cota+csca)

= sina * (cosa - sina) / cosa
+ (sina + sina/cosa) / (cosa/sina + 1/sina)

= sina - (sina)^2 / cosa
+ (sina)^2 * (1 + 1/cosa) / (1 + cosa)

= sina - (sina)^2 / cosa
+ (sina)^2 * (cosa + 1) / [ cosa * (1 + cosa) ]

= sina - (sina)^2 / cosa
+ (sina)^2 * 1 / cosa

= sina

sina/cosa(cosa-sina)+(sina+sina/cosa)(cosa/sina+1/sina)
=sina-sina^2/cosa+(1+1/cosa)*(1+cosa)
=sina-sina^2/cosa+2+cosa+1/cosa
=sina+2cosa+2

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