Клименко формула

$\sin(A\pm B)=\sin A\ \cos B\pm \cos A\ \sin B.$

$\sec ^{2}A-{\mathop {\operatorname {tg} } }^{2}A=1\ .$

$\csc ^{2}A-{\mathop {\operatorname {ctg} } }^{2}A=1\ .$

${\frac {a-b}{a+b}}={\frac {\mathop {\operatorname {tg} } \left[{\tfrac {1}{2}}(A-B)\right]}{\mathop {\operatorname {tg} } \left[{\tfrac {1}{2}}(A+B)\right]}}$