<h2>HI MATE YOUR ANSWER SHOULD BE 10/3</h2>
Tan ( A - B ) = ( tan A - tan B ) / ( 1 + tan A tan B )
tan A = 3 tan B/2
tan ( A - B ) = ((3 tan B/ 2)-tan B) / ( 1 + 3 tan² B/2)=
= (tan B/2) / ( 2 + 3 sin²B/cos²B )=
= (sin B / cos B) / (( 2cos² B+3sin²B)/cos²B)=
=( sin B cos B ) / ( 2 cos²B + 3 ( 1 - cos² B ) ) =
= (sin B cos B ) / ( 2 cos² B + 3 - 3 cos² B ) =
= ( sin 2 B ) / 2 ( 3 - cos² B ) =
= ( sin 2 B ) / ( 6 - cos² B )=
= ( sin 2 B ) / ( 5 + 1 - 2 cos² B )=
= ( sin 2 B ) / ( 5 + sin² B + cos ² B - 2 cos² B ) =
= ( sin 2 B ) / ( 5 - ( cos² B - sin² B ) ) =
= ( sin 2 B ) / ( 5 - cos 2 B ) - correct
Notice that 56° = 45° + 11°. Then
tan(56°) = sin(56°) / cos(56°)
… = sin(45° + 11°) / cos(45° + 11°)
… = (sin(45°) cos(11°) + cos(45°) sin(11°)) / (cos(45°) cos(11°) - sin(45°) sin(11°))
Recall that sin(45°) = cos(45°) = 1/√2, so we can cancel each term involving 45° :
tan(56°) = (cos(11°) + sin(11°)) / (cos(11°) - sin(11°))