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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(2x5)) = x + 5 
January 29th, 2018, 08:46 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,898 Thanks: 1093 Math Focus: Elementary mathematics and beyond  
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. 
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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