Question

if tanA=1/2,then find the value of tan2A​

Answer 1

We know that :-

$\rm \boxed { \rm sin \: 2 \theta = \frac{2tan\theta}{1 + {tan}^{2} \theta}}$

$\rm \boxed { \rm Cos \: 2 \theta = \frac{1 - {tan}^{2} \theta}{1 + {tan}^{2} \theta}}$

We also know that :-

$\rm \: tan \theta \: = \dfrac{sin \theta}{cos\theta}$

So ,

$\rm \: tan 2\theta \: = \dfrac{sin 2\theta}{cos2\theta}$

$\rm \implies tan 2\theta \: = \dfrac{\frac{2tan\theta}{1 + {tan}^{2} \theta}}{\frac{1 - {tan}^{2}\theta}{1 + {tan}^{2} \theta}} = {\dfrac{2tan\theta}{1 - {tan}^{2} \theta}}$

Therefore , now :-

$\rm \implies tan 2A \: = {\dfrac{2tanA}{1 - {tan}^{2} A}}$

Now put tan A = 1/2 ( given in the question)

$\rm \implies tan 2A \: = {\dfrac{2 \times \frac{1}{2} }{1 - { (\frac{1}{2} )}^{2} }}$

$\rm \implies tan 2A \: = {\dfrac{1 }{1 - { (\frac{1}{4} )} }}$

$\rm \implies tan 2A \: = {\dfrac{1 }{{ (\frac{4 - 1}{4} )} }} = \dfrac{1}{ \frac{3}{4} }$

$\rm \implies tan 2A \:= \dfrac{4}{3}$

Answer :

• tan 2A = 4/3