Thread: 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)

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 into the equation.

1)You would need to use angle sum formulas here:

2)And you will need to use

3)You will also use and

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