Question : If $\tan A=\frac{1}{2}$ and $\tan B=\frac{1}{3}$, then the value of $A+B$ is:
Option 1: $60^\circ$
Option 2: $15^\circ$
Option 3: $30^\circ$
Option 4: $45^\circ$
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Correct Answer: $45^\circ$
Solution :
Given: $\tan A=\frac{1}{2}$ and $\tan B=\frac{1}{3}$
We know that $\tan(A+B)=\frac{\tan A +\tan B}{1-\tan A \tan B}$
⇒ $\tan(A+B)= \frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2}\times\frac{1}{3}}$
⇒ $\tan(A+B)=1$
$\therefore(A+B)= \frac{\pi}{4}=45 ^\circ$
Hence, the correct answer is $45^\circ$.
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