Posted Tue Oct 06, 2015 8:37 pm
$cos({ \alpha}+{ \beta})=cos {\alpha}.cos {\beta}-sin {\alpha}.sin {\beta}$
$cos ({ \alpha}- \beta)=cos {\alpha} .cos{ \beta}+sin {\alpha} .sin {\beta}$
$sin ({\alpha}-\beta)=sin {\alpha} .cos {\beta}+ cos {\alpha}. sin{\beta}$
$sin ({\alpha}-\beta)=sin{\alpha}.cos{\beta}-cos{\alpha}.sin{\beta}$
$tan ({\alpha}+\beta)=\frac{tan{\alpha}+tan{\beta}}{1-tan{\alpha}.tan{\beta}}$
$tan (\alpha -\beta )=\frac{tan\alpha -tan\beta }{1+tan\alpha .tan\beta }$
$cot({\alpha}+\beta)=\frac{cot{\alpha}.cot{\beta}-1}{cot{\beta}+cot{\alpha}};cot({\alpha}-\beta)=\frac{cot{\alpha}.cot{\beta}+1}{cot{\beta}-cot{\alpha}}$
$sin{\alpha} \pm cos{\alpha}=\sqrt{2}sin({\alpha} \pm \frac{\pi}{4}); cos{\alpha} \pm sin{\alpha}=\sqrt{2}cos({\alpha} \mp \frac{\pi}{4}$
$a.sinx+b.cosx=\sqrt{a^2+b^2} (cos{\alpha}.sin x+sin{\alpha}.cos x)=\sqrt{a^2+b^2}sin(x+{\alpha})$
Với số $\alpha $ sao cho $cos{\alpha}=\frac{a}{\sqrt{a^2+b^2}} và sin{\alpha}=\frac{b}{\sqrt{a^2+b^2}}$
$cos2{\alpha}=cos^2{\alpha}-sin^2{\alpha}=2cos^2{\alpha}-1=1-2sin^2{\alpha}$
$sin2{\alpha}=2sin{\alpha}cos{\alpha} ; tan2{\alpha}=\frac{2tan{\alpha}}{1-tan^2{\alpha}}$
$cos^2{\alpha}=\frac{1+cos2{\alpha}}{2} ; sin^2{\alpha}=\frac{1-cos2{\alpha}}{2}$
$sin3{\alpha}=3sin{\alpha}-4sin^3{\alpha} ;cos3{\alpha}=4cos^3{\alpha}-3cos{\alpha}$
$sin^3{\alpha}=\frac{3sin{\alpha}-sin3{\alpha}}{4} ;cos^3{\alpha}=\frac{3cos{\alpha}+cos3{\alpha}}{4}$
$tan3{\alpha}=\frac{3tan{\alpha}-tan^3{\alpha}}{1-3tan^2{\alpha}}$
$cos{\alpha}+cos{\beta}=2cos\frac{{\alpha}+\beta}{2}cos\frac{{\alpha}-\beta}{2}$
$cos{\alpha}-cos{\beta}=-2sin\frac{{\alpha}+\beta}{2}sin\frac{{\alpha}-\beta}{2}$
$sin{\alpha}+sin{\beta}=2sin\frac{{\alpha}+\beta}{2}cos\frac{{\alpha}-\beta}{2}$
$sin{\alpha}-sin{\beta}=2cos\frac{{\alpha}+\beta}{2}sin\frac{{\alpha}-\beta}{2}$
$sin{\alpha}sin{\beta}=-\frac{1}{2}[cos({\alpha}+\beta)-cos({\alpha}-\beta)]$
$cos{\alpha}cos{\beta}=\frac{1}{2}[cos({\alpha}+\beta)+cos({\alpha}-\beta)]$
$sin{\alpha}cos{\beta}=\frac{1}{2}[sin({\alpha}+\beta)+sin({\alpha}-\beta)]$
$tan{\alpha} \pm tan{\beta}=\frac{sin({\alpha}\pm \beta)}{cos{\alpha}.cos{\beta}}$
$cot{\alpha} \pm cot{\beta}=\frac{sin(\beta \pm {\alpha})}{sin{\alpha}sin{\beta}}$