SOLUTION: Solve 6 tan θ + sec2 θ = 8

Algebra.Com
Question 733434: Solve
6 tan θ + sec2 θ = 8
Answer by Edwin McCravy(20062)   (Show Source): You can put this solution on YOUR website!
      6·tanθ + secēθ = 8

Use the identity: secēθ = 1 + tanēθ

  6·tanθ + 1 + tanēθ = 8

Get 0 on the right side and arrange in 
descending order:

   tanē + 6·tanθ - 7 = 0

That factors as:

(tanθ + 7)(tanθ - 1) = 0

tanθ + 7 = 0        tanθ - 1 = 0
    tanθ = -7           tanθ = 1

Maybe you can finish from here.  You didn't say whether you 
wanted the solutions in radians or degrees and whether you 
wanted only the solutions in the interval [0,360°), [0,2p)
or whether you wanted all infinitely many solutions by writing 
an expression in terms of integer n.

Edwin
RELATED QUESTIONS

Let csc θ = 19/6 , 0 < θ < pi/2 sinθ= 6/19 Find: cosθ, tanθ,... (answered by lwsshak3)
9. Find the values of the six trigonometric functions of the acute angle in standard... (answered by Fombitz)
prove the identity (cosθ - sinθ)/(cosθ + sinθ) = sec2θ -... (answered by Edwin McCravy)
cosθ/sinθ=1/tanθ (answered by Aswathy)
Simplify the expression. (9 - tanēθ) / (tanēθ - 5tanθ +... (answered by Edwin McCravy)
I don't know how to solve this i need to verify the identity?... (answered by Alan3354,lwsshak3)
Prove. sinēθ + tanēθ +cosēθ =... (answered by Edwin McCravy)
Prove tanθ*cot θ = secθ*cscθ (answered by solve_for_x)
tanθ*cotθ = secθ*cscθ (answered by Alan3354)