Question

if tan(A+B)=√3 and tan(A-B)=1/√3;0°<A+B<90°;A>B find A and B​

Answer 1

Answer:

A=45⁰

B=15⁰

Step-by-step explanation:

tan60⁰=root3. (1

so A+B = 60

Tan30⁰=1/√3

so A-B=30. (2

Solve both 1 and 2 (either adding or subtracting)

you get A=45⁰ and B=15⁰

Answer 2

Answer:

tan(A+B) = √3

=> tan(A+B) = tan 60°

=> A+B = 60° ...(1)

tan(A-B) 1/√3

=> tan(A-B)= tan 30°

=> A-B = 30°. ...(2)

On Adding equations (1) and (2), we get

2A = 90° => A = 90°/2 = 45°

From equation (1),

B = 60° - A = 60° - 45° = 15°

Hence, A = 45° and B = 15°.