If $\tan A=\dfrac{1}{2}$ and $\tan B=\dfrac{1}{3}$ then $\tan(2A+B)$ is equal to : (a) $3$ (b) $1$ (c) $4$ (d) $2$

If tan A=(1)/(2) and tan B=(1)/(3) then tan(2A+B) is equal to : (a) 3 (b) 1 (c) 4 (d) 2

Question 29 of 36

\tan A=\dfrac{1}{2}

(a)

3

(b)

1

(c)

4

(d)

2

Tamil Nadu DgeTamil Nadu HSC First Year (DGE) Commerce Board 2024MCQ· 1mImportance★★★★★

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With $\tan A=\tfrac12$ and $\tan B=\tfrac13$ , $\tan(2A+B)=3$ .

Step 1 — find $\tan 2A$ using the double-angle formula:

$\tan 2A=\frac{2\tan A}{1-\tan^2 A}=\frac{2\cdot\frac12}{1-\frac14}=\frac{1}{\frac34}=\frac{4}{3}.$

Step 2 — apply the compound-angle formula $\tan(2A+B)=\dfrac{\tan 2A+\tan B}{1-\tan 2A\,\tan B}$ : …