Question

15.) If tan(A+B)=v3 and tan(A-B)=1/13, 1p
then find the value of Aand B, where A
and B are acute angles and A >B*​

Answer 1

Answer :

A = 45° , B = 15°

Solution :

• Given: tan(A+B) = √3 , tan(A-B) = 1/√3
• To find: A , B = ?

We have ;

=> tan(A + B) = √3

=> tan(A + B) = tan60°

=> A + B = 60° -----------(1)

Also ,

=> tan(A - B) = 1/√3

=> tan(A - B) = tan30°

=> A - B = 30° ---------(2)

Now ,

Adding eq-(1) and (2) , we get ;

=> A + B + A - B = 60° + 30°

=> 2A = 90°

=> A = 90°/2

=> A = 45°

Now ,

Putting A = 45° in eq-(1) , we get ;

=> A + B = 60°

=> 45° + B = 60°

=> B = 60° - 45°

=> B = 15°

Hence , A = 45° and B = 15° .