SOLUTION: If tan a=1/5 and tan b=1/239, find the value of tan(4a-b)

Question 392042: If tan a=1/5 and tan b=1/239, find the value of tan(4a-b)
Answer by espeigel(1) (Show Source): You can put this solution on YOUR website!
This trig problem involves trig identities and double angle formulas. You should start with
1. tan (4a - b) = tan4a - tanb / 1 + tan4a tanb
2. tan4a = 2tan2a / 1-2tan^2 a
3. tan2a = 2tana / 1- tan^2a
= 2(1/5) / 1 - (1/25)
= (2/5) / (24/25)
= 5/12
4. tan4a = 2tan2a / 1-2tan^2 a
= 2(5/12) / (1 - 25/144)
= (5/6) / (119/144)
= 120/119
5. tan (4a - b) = tan4a - tanb / 1 + tan4a tanb
= (120/119) - (1/239) / 1 + (120/119)(1/239)
= (28561/28441) / 1 + 120/28441
= (28561/28441) / (28561/28441)
= 1
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