Question

If tan(A+B) =1/7 and tanA=1/3, find tanB

Answer 1

Answer:

-2/11

Step-by-step explanation:

tan(A+B) = (tanA + tanB)/(1- tanAtanB)

1/7 = (1/3 + tanB)/(1 - 1/3* tanB)

1/7 = (1+ 3tanB)/(3 - tanB)

22tanB = -4 => tanB = -2/11

Answer 2

GIVEN :–

$\\ \rm \: \: { \huge{.}} \: \: \tan(A + B ) = \dfrac{1}{7}$

$\\ \rm \: \: { \huge{.}} \: \: \tan(A) = \dfrac{1}{3}$

TO FIND :–

$\\ \rm \: \: { \huge{.}} \: \: \tan( B ) = ?$

SOLUTION :–

• We know that –

$\\ \: \longrightarrow\: \large { \boxed{ \rm{ \tan(A + B ) = \dfrac{ \tan(A ) + \tan(B) }{1 - \tan(A ) \tan( B) }}}}$

• Now put the values –

$\\ \: \implies\: \:{ \rm{ \dfrac{1}{7} = \dfrac{ \dfrac{1}{3} + \tan(B) }{1 - \left ( \dfrac{1}{3} \right ) \tan( B) }}}$

$\\ \: \implies\: \:{ \rm{ \dfrac{1}{7} = \dfrac{ 1+ 3 \tan(B) }{3 - \tan( B) }}}$

$\\ \: \implies\: \:{ \rm{ 3 - \tan(B) = 7 + 21 \tan(B) }}$

$\\ \: \implies\: \:{ \rm{ 3 - 7 = 22 \tan(B) }}$

$\\ \: \implies\: \:{ \rm{ - 4 = 22 \tan(B) }}$

$\\ \: \implies\: \:{ \rm{ \tan(B) = - \dfrac{4}{22} }}$

$\\ \: \implies\: \large{ \boxed{ \rm{ \tan(B) = - \dfrac{2}{11} }}}$