Answer:
[tex]\tan 90[/tex]
Explanations:
Given the trigonometric function:
[tex]\frac{\tan 100-\tan 10}{1+\tan 100\tan 10}[/tex]
According to the double angle rule in trigonometry identity;
[tex]\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}[/tex]
Comparing both expressions, you can see that:
A = 100⁰
B = 10⁰
This shows that the given trigonometry identity is equivalent to:
[tex]\tan (100-10)=\frac{\tan100-\tan10}{1+\tan100\tan10}[/tex]
Next is to write the trigonometry function tan(100-10) as a function of single number;
Since tan(100-10) = tan 90, hence;
[tex]\tan 90=\frac{\tan100-\tan10}{1+\tan100\tan10}[/tex]
