Quick Trig Question (1 Viewer)

[rama_v]

How do you solve Tan2x-3Tanx=1 ? I keep getting a cubic and it doesnt seem to work out..

 

[acmilan]

tan2x = 2tanx/(1-tan²x)

2tanx/(1-tan²x) - 3tanx = 1

2tanx - 3tanx(1-tan²x) = 1-tan²x

2tanx - 3tanx + 3tan³x = 1 - tan²x

3tan³x + tan²x - tanx - 1 = 0

Let U = tanx (for simplicity)

3U³ + U² - U - 1 = 0

If i didnt make any errors, try see if you can solve for U in that equation and the make tanx = whatever values you get for U.

 

[rama_v]

Ahh ok now I think I see what I've done wrong, it was a silly error on my part. The solution is x=36degrees 21 minutes. Thanks