Question

If tan(A+B) =√3 and tan(A-B) = 1,0°B,then find the value of A&B

Answer 1

Hi...☺

Here is your answer...✌

tan(A + B) = √3

tan(A + B) = tan 60°

=> A + B = 60° -----(1)

And,

tan(A - B) = 1

tan(A - B) = tan 45°

=> A - B = 45° -----(2)

Adding (1) and (2)
We get

2A = 105°

A = 105°/2

A = 52.5°

Putting in eq(1)
We get

52.5° + B = 60°

B = 60° - 52.5°

B = 7.5°

HENCE,

A = 52.5° and B = 7.5°

Answer 2

Hi

1 ) tan ( A + B ) = √3

tan ( A + B ) = tan 60°

A + B = 60° -----( 1 )

2 ) tan ( A - B ) = 1

tan ( A - B ) = tan 45°

A - B = 45° -----( 2 )

Add equation ( 1 ) and ( 2 ) , we get

2A = 105°

A = 52.5°

Put A = 52.5° in equation ( 1 ) ,

52.5 + B = 60

B = 60 - 52.5

B = 7.5°

I hope this helps you.

: )