Π’ΡΠΈΠ³ΠΎΠ½ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠΎΡΠΌΡΠ»Ρ
Sin (a)=2tg (a/2)/1+tg2(a/2); |. Tg (a)=2tg (a/2)/1-tg2(a/2); |. Sin2(a)+cos2(a)=1; |Sin Co Tg. Ctg (2a)=ctg2(a)-½ctg (a); |. Tg (a)-ctg (a)=-2ctg (2a); |. Tg (a)+ctg (a)=2/sin (2a); |. Ctg (a)=1-tg2(a/2)/2tg (a/2); Tg (a)ctg (a)=1; |— -+ +; 2cos (a+b/2)cos (b-a/2); |. Sin2(a/2)=1-cos (a)/2; |. Cos2(a/2)=1+cos (a)/2; |. Tg (p/2±a)=-+ctg (a). Ctg (2p±a)=±ctg (a). Sin (p±a)=-+sin (a… Π§ΠΈΡΠ°ΡΡ Π΅ΡΡ >
Π’ΡΠΈΠ³ΠΎΠ½ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠΎΡΠΌΡΠ»Ρ (ΡΠ΅ΡΠ΅ΡΠ°Ρ, ΠΊΡΡΡΠΎΠ²Π°Ρ, Π΄ΠΈΠΏΠ»ΠΎΠΌ, ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½Π°Ρ)
Π’ΡΠΈΠ³ΠΎΠ½Π°ΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠΎΡΠΌΡΠ»Ρ.
sin2(a)+cos2(a)=1; |Sin Co Tg.
tg (a)=sin (a)/cos (a); |++ -+ -+.
tg (a)ctg (a)=1; |— -+ +;
1+tg2(a)=1/cos2(a); |.
1+ctg2(a)=1/sin2(a); |sin (p/2±a)=cos (a);
|sin (p±a)=-+sin (a);
sin (a+b)=sin (a)cos (b)+cos (a)sin (b); |sin (3p/2±a)=-cos (a);
sin (a-b)=sin (a)cos (b)-cos (a)sin (b); |sin (2p±a)=±sin (a);
cos (a+b)=cos (a)cos (b)-sin (a)sin (b); |.
cos (a-b)=cos (a)cos (b)+sin (a)sin (b); |cos (p/2±a)=±sin (a);
tg (a+b)=tg (a)+tg (b)/1-tg (a)tg (b); |cos (p±a)=-cos (a);
tg (a-b)=tg (a)-tg (b)/1-tg (a)tg (b); |cos (3p/2±a)=±sin (a);
ctg (a+b)=ctg (a)ctg (b)-1/ctg (a)+ctg (b); |cos (2p±a)=cos (a);
ctg (a-b)=ctg (a)ctg (b)+1/ctg (b)-ctg (a); |.
|tg (p/2±a)=-+ctg (a).
sin (2a)=2sin (a)cos (a); |tg (p±a)=±tg (a).
cos (2a)=cos2(a)-sin2(b)=1−2sin2(a); |tg (3p/2±a)=-+ctg (a).
tg (2a)=2tg (a)/1-tg2(a); |tg (2p±a)=±tg (a).
ctg (2a)=ctg2(a)-½ctg (a); |.
sin (3a)=3sin (a)-4sin3(a); |ctg (p/2±a)=-+tg (a).
tg (3a)=3tg (a)-tg3(a)/1−3tg2(a); |ctg (p±a)=±ctg (a).
ctg (3a)=3ctg (a)-ctg3(a)/1−3ctg2(a); |ctg (3p/2±a)=-+tg (a).
|ctg (2p±a)=±ctg (a).
sin2(a/2)=1-cos (a)/2; |.
cos2(a/2)=1+cos (a)/2; |.
tg2(a/2)=1-cos (a)/1+cos (a); |.
ctg2(a/2)=1+cos (a)/1-cos (a); |.
tg (a/2)=sin (a)/1+cos (a)=1-cos (a)/sin (a); |.
ctg (a/2)=sin (a)/1-cos (a)=1+cos (a)/sin (a);|.
|.
sin (a)+sin (b)=2sin (a+b/2)cos (a-b/2); |.
sin (a)-sin (b)=2sin (a-b/2)cos (a+b/2); |.
cos (a)+cos (b)=2cos (a+b/2)cos (a-b/2); |.
cos (a)-cos (b)=-2cos (a+b/2)cos (a-b/2)= |.
=2cos (a+b/2)cos (b-a/2); |.
cos (a)+sin (b)=sqrt (2)cos (45-a); |.
cos (a)-sin (b)=sqrt (2)sin (45-a); |.
tg (a)+tg (b)=sin (a+b)/cos (a)cos (b); |.
tg (a)-tg (b)=sin (a-b)/cos (a)cos (b); |.
ctg (a)+ctg (b)=sin (a+b)/sin (a)sin (b); |.
ctg (a)-ctg (b)=sin (b-a)/sin (a)sin (b); |.
tg (a)+ctg (b)=cos (a-b)/cos (a)sin (b); |.
tg (a)-ctg (b)=-cos (a+b)/cos (a)sin (b); |.
tg (a)+ctg (a)=2/sin (2a); |.
tg (a)-ctg (a)=-2ctg (2a); |.
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sin (a)sin (b)=½(cos (a-b)-cos (a+b)); |.
cos (a)cos (b)=½(cos (a+b)+cos (a-b)); |.
sin (a)cos (b)=½(sin (a+b)+sin (a-b)); |.
|.
sin (a)=2tg (a/2)/1+tg2(a/2); |.
cos (a)=1-tg2(a/2)/1+tg2(a/2); |.
tg (a)=2tg (a/2)/1-tg2(a/2); |.
ctg (a)=1-tg2(a/2)/2tg (a/2);