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

1 Answer
Aug 22, 2016

Answer:

#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