Question

If tan (A + B) = $\sqrt{3}$ and tan (A - B) = $\frac{1}{\sqrt{3} }$, find the value of A and B if 0° < A + B < 90° and A > B.

Answer 1

ANSWER:⤵️

A =45°

B =15°

Step-by-step explanation:⤵️

tan (A+B) = √3

=> tan (A+B) = tan 60°

=> A+B = 60°

=> A = 60°-B

now,

tan (A-B) =1/√3

=> tan (A-B) = tan 30°

=> A-B = 30°

=> 60°-B-B = 30°

=> 60° - 2B = 30°

=> 2B = 60°-30°

=> 2B = 30°

=> B = 15°

now,

A-B = 30°

=> A -15° = 30°

=> A = 30° + 15°

=> A = 45°