高中数学必修四公式

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sin(A+B)=sinAcosB+cosAsinB sin(A-B)=sinAcosB-sinBcosA cos(A+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB

tan(A+B)=(tanA+tanB)/(1-tanAtanB) tan(A-B)=(tanA-tanB)/(1+tanAtanB) ctg(A+B)=(ctgActgB-1)/(ctgB+ctgA) ctg(A-B)=(ctgActgB+1)/(ctgB-ctgA)

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tan2A=2tanA/(1-tan2A) ctg2A=(ctg2A-1)/2ctga

cos2a=(cos^2)a-(sin^2)a=2(cos^2)a-1=1-2(sin^2)a °ë½Ç¹«Ê½

sin(A/2)=¡Ì((1-cosA)/2) sin(A/2)=-¡Ì((1-cosA)/2) cos(A/2)=¡Ì((1+cosA)/2) cos(A/2)=-¡Ì((1+cosA)/2)

tan(A/2)=¡Ì((1-cosA)/((1+cosA)) tan(A/2)=-¡Ì((1-cosA)/((1+cosA)) ctg(A/2)=¡Ì((1+cosA)/((1-cosA)) ctg(A/2)=-¡Ì((1+cosA)/((1-cosA))

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2sinAcosB=sin(A+B)+sin(A-B) 2cosAsinB=sin(A+B)-sin(A-B) 2cosAcosB=cos(A+B)-sin(A-B) -2sinAsinB=cos(A+B)-cos(A-B)

sinA+sinB=2sin((A+B)/2)cos((A-B)/2 cosA+cosB=2cos((A+B)/2)sin((A-B)/2) tanA+tanB=sin(A+B)/cosAcosB tanA-tanB=sin(A-B)/cosAcosB ctgA+ctgBsin(A+B)/sinAsinB -ctgA+ctgBsin(A+B)/sinAsinB

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1+2+3+4+5+6+7+8+9+¡-+n=n(n+1)/2 1+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

ÕýÏÒ¶¨Àí a/sinA=b/sinB=c/sinC=2R ×¢£º ÆäÖÐ R ±íʾÈý½ÇÐεÄÍâ½ÓÔ²°ë¾¶

ÓàÏÒ¶¨Àí b2=a2+c2-2accosB ×¢£º½ÇBÊDZßaºÍ±ßcµÄ¼Ð½Ç

»¡³¤¹«Ê½ l=a*r aÊÇÔ²ÐĽǵĻ¡¶ÈÊýr >0 ÉÈÐÎÃæ»ý¹«Ê½ s=1/2*l*r

³Ë·¨ÓëÒòʽ·Ö a2-b2=(a+b)(a-b) a3+b3=(a+b)(a2-ab+b2) a3-b3=(a-b(a2+ab+b2)

Èý½Ç²»µÈʽ |a+b|¡Ü|a|+|b| |a-b|¡Ü|a|+|b| |a|¡Üb<=>-b¡Üa¡Üb

|a-b|¡Ý|a|-|b| -|a|¡Üa¡Ü|a|

Ò»Ôª¶þ´Î·½³ÌµÄ½â -b+¡Ì(b2-4ac)/2a -b-¡Ì(b2-4ac)/2a

¸ùÓëϵÊýµÄ¹Øϵ X1+X2=-b/a X1*X2=c/a ×¢£ºÎ¤´ï¶¨Àí

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b2-4ac=0 ×¢£º·½³ÌÓÐÁ½¸öÏàµÈµÄʵ¸ù b2-4ac>0 ×¢£º·½³ÌÓÐÁ½¸ö²»µÈµÄʵ¸ù

b2-4ac<0 ×¢£º·½³ÌûÓÐʵ¸ù£¬Óй²éÊý¸ù ½µÃݹ«Ê½

£¨sin^2£©x=1-cos2x/2 £¨cos^2£©x=i=cos2x/

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Áîtan(a/2)=t sina=2t/(1+t^2)

cosa=(1-t^2)/(1+t^2) tana=2t/(1-t^2)