Answer
- Similarity: both contain $\tan A$ and $\tan B$ in the numerator and $1$ and $\tan A\tan B$ in the denominator.
- Difference: In $\tan (A-B)$, in the numerator, $\tan B$ is subtracted from $\tan A$. In the denominator, $1$ and $\tan A\tan B$ are summed together. At the same time, in $\tan (A+B)$, the reverse is true.
Work Step by Step
- Formula for $\tan(A-B)$
$$\tan(A-B)=\frac{\tan A- \tan B}{1+\tan A\tan B}$$
- Formula for $\tan (A+B)$
$$\tan(A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}$$
Again, the content of each formula is the same. Both $\tan (A-B)$ and $\tan (A+B)$ contain $\tan A$ and $\tan B$ in the numerator and $1$ and $\tan A\tan B$ in the denominator.
The difference is again about the signs.
- In $\tan (A-B)$, in the numerator, $\tan B$ is subtracted from $\tan A$. In the denominator, $1$ and $\tan A\tan B$ are summed together.
- In $\tan (A+B)$, the reverse is true. In the numerator, $\tan A$ and $\tan B$ are added together. In the denominator, $\tan A\tan B$ is subtracted from $1$.
