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Math Help - Solution of trigonometric equation?

  1. #1
    Super Member fardeen_gen's Avatar
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    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)
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  2. #2
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    Quote Originally Posted by fardeen_gen View Post
    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 \pi n + \arctan 3 into the equation.

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

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

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

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