Question

if tan ( A + B ) = √3 and tan ( A - B ) = 1/√3 , A>B , then find the value of A ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ​

Answer 1

$\huge\bold{Question:-}$

• If tan (A + B) =√3 and tan (A - B) =$\frac{1}{ \sqrt{3} }$
• Find the Value of A

$\huge\bold{Solution:-}$

Given,

$\tan \:( A + B) = \sqrt{3}$

$\tan \: (A - B) = \frac{1}{ \sqrt{3} }$

We know that

$\tan \: 60 \degree = \sqrt{3}$

$\tan 30\degree = \frac{1}{ \sqrt{3} }$

So,

(A + B) = 60°_______(1)

(A - B) = 30°_______(2)

Solving (1) and (2)

A + B = 60°

(+) A - B = 30°

-----------------

2A = 90°

-----------------

$A \: = \frac{90}{2} = 45 \degree$

Hope this is helpful✓

Answer 2

ANSWER :- A = 45 °, B = 15°

$tan ( A+ B ) = √3$

$(A+ B) = tan {}^{ - 1} ( \sqrt{3} )$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: A+ B = 60 {} \: ^{0} - - - - - (1)$

$tan ( A - B ) = \frac{1}{√3}$

$(A-B) = tan^{-1} \frac{1}{√3}$

$(A - B ) = 30° - - - - - - (2)$

A + B = 60°----------------(1)

A - B = 30°-----------------(2)

(1)+(2)

$\implies$

$2A = 90°$

$\implies \: A \: = \frac{90}{2}$

$\implies45°$

$\implies \: A + B = 60$

$\implies \: B \: = 60 - 45 \\ = 15°$