Question

1
5
(6) If tan A=
6
A+B=*
and tan B
then show that A + B =
4
11​

Answer 1

Step-by-step explanation:

Correct Question :-

If tanA = 5/6 , tanB = 1/11 . Then show that 'A + B' = π/4

Given,

tanA = 5/6

tanB = 1/11

To Prove :-

A + B = π/4

How To Do :-

As they given the values of both 'tanA' and 'tanB' we need to substitute those values in the formula of 'tan(A + B)' then after simplifying we can get the value of tan(A + B) then by cancelling 'tan' on both sides we can get the value of 'A + B'.

Formula Required :-

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

Solution :-

Substituting value of tanA and tanB in the formula :-

$tan(A + B) = \dfrac{\dfrac{5}{6}+\dfrac{1}{11}}{1-\left(\dfrac{5}{6}\right)\left(\dfrac{1}{11}\right)}$

$= \dfrac{ \dfrac{5(11) + 1(6)}{66} }{1 - \dfrac{5 \times 1}{6 \times 11} }$

$= \dfrac{ \dfrac{55 + 6}{66} }{1 - \dfrac{5}{66} }$

$= \dfrac{ \dfrac{61}{66} }{1 - \dfrac{5}{66} }$

$= \dfrac{ \dfrac{61}{66} }{ \dfrac{66 - 5}{66} }$

$= \dfrac{ \dfrac{61}{66} }{ \dfrac{61}{66} }$

$= \dfrac{61}{66} \times \dfrac{61}{66}$

tan(A + B) = 1

tan(A + B) = tan45°

cancelling 'tan' on both sides :-

A + B = 45°

A + B = π/4

[ 45° = π/4 ]

Hence Proved.