# Trigonometry solutions Question

#### PhamCy

Here's the question.
Find the solutions of the equation tan(x)=2cos(x)+1 if 0 ≤ x ≤ 2π.
I know this question can be solved by observing the graph but is there any other ways (like algorithms OR some Trigonometry rules) to solve this, I couldn't figure that out.
Thank you for those who noticed my question.

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#### BvU

Homework Helper
Hello PhamCy, !

For example: substitute $\tan x = {\sin x\over \cos x}$ and see where it leads you

#### mfb

Mentor
Way beyond what you can solve analytically with high school mathematics. WolframAlpha knows how to solve it analytically, here is one of the solutions:

#### BvU

Homework Helper
Oops, I 'missed' the +1 which makes things difficult

#### vela

Staff Emeritus
Homework Helper
You could express the relationship as a polynomial in $\cos\theta$, and then find the roots of the polynomial using something like Newton's method.

#### hunt_mat

Homework Helper
Turn everything into $\cos x$ to get:
$$4\cos^{4}x+4\cos^{3}x+2\cos^{2}x-1=0$$
From here solve it using whatever method you like. I would advise you plotting the polynomial first.

"Trigonometry solutions Question"

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