Question

if tan(a+b)=√3, and tan(a-b)=√1/3 find a and b​

Answer 1

Answér :

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° , b = 15°