If tanA=(1/2), tanB=(1/3), then tan(2A+B) is equal to

Question

If tanA=(1/2), tanB=(1/3), then tan(2A+B) is equal to (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

Given, tanA=(1/2), tanB=(1/3) ldots(i) Now, tan(2A+B)=(tan 2A+tan B/1-tan 2A tan B) =((2 tan A/1-tan2 A)+tan B/1-(2 tan A)1-tan2 A× tan B) =((4/3)+(1/3)/1-(4)3×(1)3=3

Q. If $t an A = \frac{1}{2}$ , $t an B = \frac{1}{3}$ , then $t an (2 A + B)$ is equal to

$1$

$2$

$3$

$4$

Q. If tanA=21​, tanB=31​, then tan(2A+B) is equal to

1

2

3

4

Given, tanA=21​,tanB=31​…(i) Now, tan(2A+B)=1−tan2AtanBtan2A+tanB​ =1−1−tan2A2tanA​×tanB1−tan2A2tanA​+tanB​ =1−34​×31​34​+31​​=3

Q. If $t an A = \frac{1}{2}$ , $t an B = \frac{1}{3}$ , then $t an (2 A + B)$ is equal to

$1$

$2$

$3$

$4$