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• $sin(-a)=-sin(a)$
• $cos(-a)=cos(a)$
• $sin(\pi/2-a)=cos(a)$
• $cos(\pi/2-a)=sin(a)$
• $sin(\pi/2+a)=cos(a)$
• $cos(\pi/2+a)=-sin(a)$
• $sin(\pi-a)=sin(a)$
• $cos(\pi-a)=-cos(a)$
• $sin(\pi+a)=-sin(a)$
• $cos(\pi+a)=-cos(a)$
• $tg(a)=tan(a)= \frac{sin(a)}{cos(a)}$

• $sin(a+b)=sin(a)cos(b)+\cos(a)\sin(b)$
• $sin(a-b)=sin(a)cos(b)-cos(a)sin(b)$
• $cos(a+b)=cos(a)cos(b)-sin(a)sin(b)$
• $cos(a-b)=cos(a)cos(b)+sin(a)sin(b)$

• $tan(\alpha +\beta )=\frac{tan\alpha +tan\beta }{1-tan\alpha tan\beta }$
• $tan(\alpha -\beta )=\frac{tan\alpha -tan\beta }{1+tan\alpha tan\beta }$

• $sin{a}+sin(b) =2 sin{\frac{a+b}{2}} cos{\frac{a-b}{2}}$
• $sin{a}-sin{b} = 2 cos{\frac{a+b}{2}} sin{\frac{a-b}{2}}$
• $cos(a)+cos(b) =2 cos{\frac{a+b}{2}} cos{\frac{a-b}{2}}$
• $cos(a)-cos(b) =-2 sin{\frac{a+b}{2}} sin{\frac{a-b}{2}}$

• $sin(a)sin(b)=-\frac{1}{2} [cos(a+b)-cos(a-b)]$
• $cos(a)cos(b)=\frac{1}{2} [cos(a+b)+cos(a-b)]$
• $sin(a)cos(b)=\frac{1}{2} [sin(a+b)+sin(a-b)]$
• $cos(a)sin(b)=\frac{1}{2} [sin(a+b)-sin(a-b)]$

• $sin(2a)=2sin(a)cos(a)$
• $cos(2a)=cos^2(a)-sin^2(a)=2cos^2(a)-1=1-2sin^2(a)$

• $sin^2(\frac{a}{2})=\frac{1-cos(a)}{2}$
• $cos^2(\frac{a}{2})=\frac{1+cos(a)}{2}$
• $tg(\frac{a}{2})=\frac{1-cos(a)}{sin(a)}=\frac{sin(a)}{1+cos(a)}$

• $sin(a)= \frac{2tan(\frac{a}{2})}{1+tan^2(\frac{a}{2})}$
• $cos(a)= \frac{1-tan^2(\frac{a}{2})}{1+tan^2(\frac{a}{2})}$
• $tg(a)=tan(a)= \frac{2tan(\frac{a}{2})}{(1-tan^2(\frac{a}{2})}$

• $a*sin(a)+b*cos(a)=sqrt(a^2+b^2)sin(a+c)$ 其中 $tan(c)=b/a$
• $a*sin(a)-b*cos(a)=sqrt(a^2+b^2)cos(a-c)$ 其中 $tan(c)=a/b$
• $1+sin(a)=(sin(a/2)+cos(a/2))^2$
• $1-sin(a)=(sin(a/2)-cos(a/2))^2$

# 其他非重点

• $csc(a)=1/sin(a)$
• $sec(a)=1/cos(a)$