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 January 29th, 2018, 07:25 AM #1 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry [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?
 January 29th, 2018, 07:39 AM #2 Senior Member   Joined: Dec 2015 From: holland Posts: 163 Thanks: 37 Math Focus: tetration cot(x) is not the same as 1/(tan(x)) you can write the eq as tan(tan(2x-5)) = x + 5
January 29th, 2018, 08:46 AM   #3
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Quote:
 Originally Posted by manus cot(x) is not the same as 1/(tan(x))
1/tan(x) = 1/(sin(x)/cos(x)) = cos(x)/sin(x) = cot(x)

 January 29th, 2018, 01:04 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,098 Thanks: 1905 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. Thanks from Monox D. I-Fly
 January 29th, 2018, 04:56 PM #5 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry Thank you skipjack!

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