Question

if tan(A+B)=1 and tan (A-B)=1/√3, 0°<A+B<90°,A>B, then find the value of A and B​

Answer 1

Answer:

A = 37.5°   and  B = 7.5°

Step-by-step explanation:

tan(A + B) = 1

tan(A + B) = tan45°

     A + B = 45°            ...(1)

tan(A - B) = 1/√3

tan(A - B) = tan30°

     A - B = 30°              ...(2)

Adding (1) and (2):

⇒ (A + B) + (A - B) = 45° + 30°

⇒ 2A = 75°

⇒ A = 75/2

⇒ A = 37.5°

     Thus, A - B = 30°    ⇒ 37.5° - 30° = B

                                     ⇒ 7.5° = B

Note that if tan(A + B) = √3,

A = 45°   &   B = 15°   , following the same procedure

Answer 2

tan(a+b)=tan45

a+b=45

a=45-b

a-b=30

45-b-b=30

2b=15

b=15/2

a=75/2