Question

If tan(A + B) = √3 and tan(A - B)=1/√3, 0° <A+B ≤ 90° find the A and B.

Answer 1

Answer:

tan(A+B)=√3=tan 60°

=> A+B=60

tan(A-B)=1/√3=tan30°

=> A-B=30

so,

A+B=60

A-B=30

adding,2A=90

=> A=90/2=45

A+B=60

=> 45+B=60

=> B=60-45=15

A=45° , B=15°

Answer 2

$✅❤️Answer❤️$

Given tan(A+B)=3

⟹A+B=60°⋯(1)

tan(A−B)=

$\frac{1}{3}$

⟹A−B=30° ⋯(2)

(1)+(2)⟹2A=90°

⟹A=45°

Put A value in (1)

⟹B=60°−45°

⇒B=15°