Drummondjacob

Compound Angle Formulae

$\sin(x+y)=\sin(x)\times \cos(y)+\cos(x)\times \sin(y)\,\!$
$\sin(x-y)=\sin(x)\times \cos(y)-\cos(x)\times \sin(y)\,\!$
$\cos(x+y)=\cos(x)\times \cos(y)-\sin(x)\times \sin(y)\,\!$
$\cos(x-y)=\cos(x)\times \cos(y)+\sin(x)\times \sin(y)\,\!$
$\tan(x+y)={\frac {\tan(x)+\tan(y)}{1-\tan(x)\times \tan(y)}}$
$\tan(x-y)={\frac {\tan(x)-\tan(y)}{1-\tan(x)\times \tan(y)}}$
$\cot(x+y)={\frac {\cot(x)\times \cot(y)-1}{\cot(x)+\cot(y)}}$
$\cot(x-y)={\frac {\cot(x)\times \cot(y)+1}{\cot(y)-\cot(x)}}$

Amortization Formula resolution

Original

$A=P\left(r+{\frac {r}{(1+r)^{n}-1}}\right)$

Attempt 2: Work in progress

$A=P\left(r+{\frac {r}{(1+r)^{n}-1}}\right)$

$r+{\frac {r}{(1+r)^{n}-1}}={\frac {P}{A}}$

${\frac {r}{(1+r)^{n}-1}}={\frac {P}{A}}-r$

Attempt 1: Failure

$A=Pr\left(1+{\frac {1}{(1+r)^{n}-1}}\right)$

${\frac {A}{Pr}}=1+{\frac {1}{(1+r)^{n}-1}}$