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January 29th, 2018, 06:25 AM   #1
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[ASK] Trigonometric Equation

If 0 < x < 90, what is the solution of tan(2x - 5) = cot(x + 5)?
I got stuck in tan(2x - 5)tan(x + 5) = 1. What should I do after that?
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January 29th, 2018, 06:39 AM   #2
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cot(x) is not the same as 1/(tan(x))
you can write the eq as tan(tan(2x-5)) = x + 5
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January 29th, 2018, 07:46 AM   #3
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Quote:
Originally Posted by manus View Post
cot(x) is not the same as 1/(tan(x))
1/tan(x) = 1/(sin(x)/cos(x)) = cos(x)/sin(x) = cot(x)
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January 29th, 2018, 12:04 PM   #4
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tan(2x - 5) = cot(x + 5) = tan(90 - (x + 5)), so 2x - 5 = 90 - x - 5 + 180k, where k is an integer.

Hence x = 30 + 60k.

So that 0 < x < 90, k = 0, and so x = 30.

As tan(2x - 5)tan(x + 5) = 1, (tan(2x - 5) + tan(x + 5))/(1 - tan(2x - 5)tan(x + 5)) is undefined,
which implies tan(3x) is undefined, and so x = 30.
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January 29th, 2018, 03:56 PM   #5
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Thank you skipjack!
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