高一数学题 三角函数诱导公式

\u3010\u9ad8\u4e00\u6570\u5b66\u3011\u4e09\u89d2\u51fd\u6570\u7684\u8bf1\u5bfc\u516c\u5f0f\u9898\u76ee

1\u3001
cos\uff08\u03c0+a\uff09=-cosa=-1/2,
cosa=1/2
a\u5728\u7b2c\u56db\u8c61\u9650
\u6240\u4ee5sina<0
sin²a+cos²a=1
sina=-\u221a3/2
sin(2\u03c0-a)=sin(-a)=-sina=\u221a3/2


2\u3001

sin(2\u03c0-a)=sin(-a)=-sina
5cos\uff082\u03c0-a\uff09/2cos(\u03c0+a)=5cos(-a)/2(-cosa)=5cosa/(-2cosa)=-5/2
sin(-a)=-sina
\u6240\u4ee5\u539f\u5f0f=-sina-5/2+sina=-5/2



3\u3001
cos(5\u03c0/6+a)=cos[\u03c0-(\u03c0/6-a)]=-cos(\u03c0/6-a)=-\u221a3/3
sin²(a-\u03c0/6)=sin²(\u03c0/6-a)=1-cos²(\u03c0/6-a)=2/3
\u6240\u4ee5\u539f\u5f0f=(-2-\u221a3)/3

\u6655,\u76f4\u63a5\u95ee\u6211\u561b
cos^2(\u03c0-x)+sin(\u03c0+x)\u00b7cos(\u03c0-x)+2sin^2(x-\u03c0)
=cosx^2+(-sinx)(-cosx)+2sinx^2
=(1+2tanx+2tanx^2)/(1+tanx^2)
\u5c061\u91cc\u7684tanx\u7b97\u51fa\u4ee3\u5165\u5c31\u884c\u4e86

1.cos(a-π/2)/sin(5π/2 +a) × sin(a-2π) × cos(2π-a)
解：原式=sina/sin(π/2+a )× sin(a) × cos(-a)
=sina/cos(a )× sin(a) × cos(a)
=sin^2(a)

2.cos²（-a）- tan(360°+a)/sin(-a)
解：原式=cos²（a）- tan(+a)/[-sin(a)]
=cos²（a）+ tan(a)/sin(a)
=cos²（a）+ 1/cos(a)

cos(a-π/2)/sin(5π/2 +a) × sin(a-2π) × cos(2π-a)
=cosa/sin(π/2+a)×sina × cosa
=cosa/cosa ×sina × cosa
=sinacosa

.cos²（-a）- tan(360°+a)/sin(-a)
=cos²a+tana/sina
=cos²a+1/cosa
=（cos³a+1）/cosa

1.cos(a-π/2)/sin(5π/2 +a) × sin(a-2π) × cos(2π-a)
=cos(π/2-a)/sin(π/2 +a) × sina × cos(-a)
=sina/sin(π-π/2-a) × sina × cosa
=sina/sin(π/2-a) × sina × cosa
=sina/cosa × sina × cosa
=sin²a
2.cos²（-a）- tan(360°+a)/sin(-a)
=cos²a+ tana/sina
=cos²a+ 1/cosa