Trig Addition Formulas

The trig addition formulas can be useful to simplify a complicated expression, or perhaps find an exact value when you only have a small table of trig values. For example, if you want the sine of 15 degrees, you can use a subtraction formula to compute sin(15) as sin(45-30).

$$ \sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b) $$ $$ \sin(a-b)=\sin(a)\cos(b)-\cos(a)\sin(b) $$ $$ \cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b) $$ $$ \cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b) $$ $$ \tan(a+b)=\frac{\tan(a)+\tan(b)}{1-\tan(a)\tan(b)} $$ $$ \tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)} $$