sederhanakan {Tan (a+b) - Tan (a-b)} ÷ {1+ tan (a+b).tan(a-b)

[tex]\displaystyle \text{misal :}\\a+b=x\\a-b=y\\\\\frac{\tan(a+b)-\tan(a-b)}{1+\tan(a+b)\tan(a-b)}=\frac{\tan x-\tan y}{1+\tan x\tan y}\\\frac{\tan(a+b)-\tan(a-b)}{1+\tan(a+b)\tan(a-b)}=\tan(x-y)\\\frac{\tan(a+b)-\tan(a-b)}{1+\tan(a+b)\tan(a-b)}=\tan(a+b-(a-b))\\\frac{\tan(a+b)-\tan(a-b)}{1+\tan(a+b)\tan(a-b)}=\tan(a+b-a+b)\\\boxed{\boxed{\frac{\tan(a+b)-\tan(a-b)}{1+\tan(a+b)\tan(a-b)}=\tan2b}}[/tex]