Question

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

Answer 1

Hi ,

we know that ,

tan 60° = √3 ----( 1 )

tan 90° = 1 -----( 2 )

Now ,

tan (A + B ) = √3

= tan 60°

A + B = 60° ----( 3 )

tan ( A - B ) = 1

= tan 90°

A - B = 90 ----- ( 4 )

add equation ( 1 ) & ( 2 ) , we get

2A = 150

A = 75 °

put A = 75° in equation ( 1 ) , we get

B = -15°

Therefore ,

A = 75°

B = - 15°

I hope this helps you.

:)