sin ( x + y ) = sin ( x ) × cos ( y ) + cos ( x ) × sin ( y ) {\displaystyle \sin(x+y)=\sin(x)\times \cos(y)+\cos(x)\times \sin(y)\,\!} sin ( x − y ) = sin ( x ) × cos ( y ) − cos ( x ) × sin ( y ) {\displaystyle \sin(x-y)=\sin(x)\times \cos(y)-\cos(x)\times \sin(y)\,\!} cos ( x + y ) = cos ( x ) × cos ( y ) − sin ( x ) × sin ( y ) {\displaystyle \cos(x+y)=\cos(x)\times \cos(y)-\sin(x)\times \sin(y)\,\!} cos ( x − y ) = cos ( x ) × cos ( y ) + sin ( x ) × sin ( y ) {\displaystyle \cos(x-y)=\cos(x)\times \cos(y)+\sin(x)\times \sin(y)\,\!} tan ( x + y ) = tan ( x ) + tan ( y ) 1 − tan ( x ) × tan ( y ) {\displaystyle \tan(x+y)={\frac {\tan(x)+\tan(y)}{1-\tan(x)\times \tan(y)}}} tan ( x − y ) = tan ( x ) − tan ( y ) 1 − tan ( x ) × tan ( y ) {\displaystyle \tan(x-y)={\frac {\tan(x)-\tan(y)}{1-\tan(x)\times \tan(y)}}} cot ( x + y ) = cot ( x ) × cot ( y ) − 1 cot ( x ) + cot ( y ) {\displaystyle \cot(x+y)={\frac {\cot(x)\times \cot(y)-1}{\cot(x)+\cot(y)}}} cot ( x − y ) = cot ( x ) × cot ( y ) + 1 cot ( y ) − cot ( x ) {\displaystyle \cot(x-y)={\frac {\cot(x)\times \cot(y)+1}{\cot(y)-\cot(x)}}}
A = P ( r + r ( 1 + r ) n − 1 ) {\displaystyle A=P\left(r+{\frac {r}{(1+r)^{n}-1}}\right)}
r + r ( 1 + r ) n − 1 = P A {\displaystyle r+{\frac {r}{(1+r)^{n}-1}}={\frac {P}{A}}}
r ( 1 + r ) n − 1 = P A − r {\displaystyle {\frac {r}{(1+r)^{n}-1}}={\frac {P}{A}}-r}
A = P r ( 1 + 1 ( 1 + r ) n − 1 ) {\displaystyle A=Pr\left(1+{\frac {1}{(1+r)^{n}-1}}\right)}
A P r = 1 + 1 ( 1 + r ) n − 1 {\displaystyle {\frac {A}{Pr}}=1+{\frac {1}{(1+r)^{n}-1}}}
