高中生必背数学公式

1.两个角之和的公式sin(a+b)= Sina cosb+cosa sinb sin(a-b)= Sina cosb-sinb cosa

cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb

tan(A+B)=(tanA+tanB)/(1-tanA tanB)tan(A-B)=(tanA-tanB)/(1+tanA tanB)

ctg(A+B)=(ctgActgB-1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+1)/(ctg B-ctgA)

倍角公式tan2a = 2 tana/(1-tan2a)ctg2a =(ctg2a-1)/2c TGA

COS2A = COS2A-SIN2A = 2 COS2A-1 = 1-2 SIN2A/2，半角公式SIN(a/2)=√((1-COSA)/2)SIN(a/2)=-√((1-COSA)/2)

cos(A/2)=√((1+cosA)/2)cos(A/2)=-√((1+cosA)/2)

tan(A/2)=√((1-cosA)/((1+cosA))tan(A/2)=-√((1-cosA)/((1+cosA))

CTG(A/2)=√((1+COSA)/((1-COSA))CTG(A/2)=-√((1+COSA))/3，差积2西纳·COSB = SIN(A+B)

2 cosa cosb = cos(A+B)-sin(A-B)-2 sinasinb = cos(A+B)-cos(A-B)

sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2 cosA+cosB = 2 cos((A+B)/2)sin((A-B)/2)

tanA+tanB = sin(A+B)/cosa cosb tanA-tanB = sin(A-B)/cosa cosb

ctgA+ctgBsin(A+B)/Sina sin B-ctgA+ctgBsin(A+B)/Sina sinb/

4.前N项和1+2+3+4+5+6+7+8+9+…+N = N(N+1)/21+3+5+7+9+11+13+15+…+(2n-1)= N * 2。

2+4+6+8+10+12+14+…+(2n)= n(n+1)12+22+32+42+52+62+72+82+…+N2 = n(n+1)(2n+1)/6

13+23+33+43+53+63+…n3 = N2(n+1)2/4 1 * 2+2 * 3+3 * 4+4 * 5+5 * 6+6 * 7+…+n(n+1)= n(n+1)(n+2)/3

5.圆的一般方程x2+y2+Dx+Ey+F=0注:D2+E2-4F>0

6.抛物线标准方程Y2 = 2PXY2 =-2PXX2 = 2PXX2 =-2Py

7.直棱镜的横向面积S=c*h，斜棱镜的横向面积S=c*h

8.正棱锥的侧面面积S=1/2c*h，正棱锥的侧面面积S=1/2(c+c)h

9.圆台侧面面积S=1/2(c+c)l=pi(R+r)l球的表面积S=4pi*r2