# Thread: Solution of trigonometric equation?

1. ## Solution of trigonometric equation?

Find which of the number nπ - arctan 3, where n is an integer, are solutions of the equation 12 tan x + [10/cos x] + 1 = 0.

Ans: n = (2k + 1)π - arctan 3, k belongs to Z

How to solve this problem? I apologize for the poor grammar in the question.(this is exactly what is written in the source)

2. Originally Posted by fardeen_gen
Find which of the number nπ - arctan 3, where n is an integer, are solutions of the equation 12 tan x + [10/cos x] + 1 = 0.

Ans: n = (2k + 1)π - arctan 3, k belongs to Z

How to solve this problem? I apologize for the poor grammar in the question.(this is exactly what is written in the source)
Just substitute $\displaystyle \pi n + \arctan 3$ into the equation.

1)You would need to use angle sum formulas here: $\displaystyle \tan (x-y),\cos(x-y)$

2)And you will need to use $\displaystyle \cos (\arctan x) = \frac{1}{\sqrt{x^2+1}}$

3)You will also use $\displaystyle \tan (\pi n) = 0$ and $\displaystyle \cos (\pi n) = (-1)^n$

As you can see #3 is saying it depends on where $\displaystyle n$ is even or odd. Which is not supprising why your answer depends only on odd numbers.