Question

How do you determine the value of tan B if tan(135 deg + B) =5?

Answer 1

`tan B = -3/2`

Explanation:

Use the trig identity:
`tan (A + B) = (tan A + tan B)/(1 - tan A.tan B)`
`tan (135 + B) = (tan 135 + tan B)/(1 - tan 135.tan B)`
Trig table of special arc gives: tan 135 = -1
There for:
`tan (135 + B) = 5 = (-1 + tan B)/(1 + tan B)`
Cross multiply:
5 + 5tan B = -1 + tan B
4tan B = -1 - 5 = - 6
`tan B = -6/4 = -3/2`
Check by calculator:
`tan B = -3/2`. --> `B = - 56^@31` --> tan (135 - 56.31) =
`= tan (78^@69) = 5`. OK