SOLUTION: Given that tan θ − cot θ = 2, find the possible values of tan θ, giving your answers in an exact form. Hence solve the equation tan θ &#872

Algebra ->  Trigonometry-basics -> SOLUTION: Given that tan θ − cot θ = 2, find the possible values of tan θ, giving your answers in an exact form. Hence solve the equation tan θ &#872      Log On


   

Question 992819: Given that tan θ − cot θ = 2,
find the possible values of tan θ, giving your answers in an exact form.
Hence solve the equation
tan θ − cot θ = 2
giving all values of θ between 0 and 360
I'm very confused how the questions are different? I really don't understand what the first question is asking me to do.

Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let  x  be  tan(x):   x = tan(x).

Then  cot(x) = 1%2Fx,  and you have an equation

x - 1%2Fx = 2.

Simplify and solve it:

x%5E2 - 2x - 1 = 0,

%28x-1%29%5E2 = 0.

The root is   x = 1.

Thus  tan(x) = 1.

x = pi%2F4 = 45°  and/or  x = pi%2F4+%2B+pi = 5pi%2F4 = 225°.