Question

. If tan(A – B) = 1/√3 and tan (A + B) = √3, find A and B, where A and B are acute angles​

Answer 1

Answer :

A = 45° , B = 15°

Solution :

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

We have ;

=> tan(A - B) = 1/√3

=> tan(A - B) = tan30°

=> A - B = 30° -------(1)

Also ,

=> tan(A + B) = √3

=> tan(A + B) = tan60°

=> A + B = 60° ------(2)

Now ,

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

=> A - B + A + B = 30° + 60°

=> 2A = 90°

=> A = 90°/2

=> A = 45°

Now ,

Putting A = 45° in eq-(2) , we get ;

=> A + B = 60°

=> 45° + B = 60°

=> B = 60° - 45°

=> B = 15°

Hence ,

A = 45° , B = 15°

Answer 2

$\huge{\boxed{\rm{Question}}}$

If tan(A – B) = 1/√3 and tan (A + B) = √3. Find A and B , where A and B are acute angles.

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• Tan(A – B) = 1/√3

• Tan (A + B) = √3

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• Value of A and B.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• Value of A = 45°

• Value of B = 15°

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: first}}}}$

• This question says that there are 2 variables = Tan(A – B) = 1/√3 and Tan (A + B) = √3. In this question we have to find the value of A and B.

$\large{\boxed{\boxed{\sf{How \: to \: do \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Let's \: see \: the \: procedure \: now}}}}$

• Firstly we know the values which are given in this question we have to write it and afterwards we have to put the cake when we put value in equation 1 we get result that is 45 degrees and that we have to substitute 45 in equation 2 after that putting the values we get result that is 15 degree. Thats why a = 45 degrees and b = 15 degree.

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

According to the question, let's carry on

Firstly ,

✂ Tan (A – B) = 1/√3

✂ Tan (A - B) = tan 30°

✂ A - B = 30° Eǫᴜᴀᴛɪᴏɴ ❶

Secondly ,

✂ Tan (A + B) = √3

✂ Tan (A + B) = tan 60°

✂ A + B = 60° Eǫᴜᴀᴛɪᴏɴ ❷

Now we have to add Equation ❶ and Equation ❷ we get the following results

☛ A - B + A + B = 30° + 60°

☛ 2A = 30° + 60°

{ We don't write B or -B here because + and - cut each other } { That's why we don't write any B here }

☛ 2A = 90°

☛ A = 90°/2

☛ A = 45°

Hence, A = 45°

Now, we have to substitute the value of Equation 1 that is 45° in Equation 2

☛ A + B = 60°

☛ 45° + B = 60°

☛ B = 60° - 45°

☛ B = 15°

Hence, B = 15°