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 August 22nd, 2018, 09:53 AM #1 Member   Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2 Trigonometry identities I need detailed solutions for the equation tan^2(x+45)=5 for 0
 August 22nd, 2018, 10:45 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2203 As tan(x + 45$^\circ$) = ±√5, you can calculate possible values for x + 45$^\circ$, namely ±65.9$^\circ$ approximately. What progress can you make from there? August 22nd, 2018, 11:45 AM #3 Member   Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2 I don't understand please make it simpler&understandable August 22nd, 2018, 05:37 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2203 tan²(x+45$^\circ$) = 5 implies tan(x+45$^\circ$) = ±√5. Do you understand that? By use of a calculator, tan$^{-1}$(±√5) = ±65.9$^\circ$ approximately. Do you also understand that? Are you aware that tan(A) = tan(A ± k(180$^\circ$)) for any integer value of k and any value of A for which tan(A) is defined? August 22nd, 2018, 09:30 PM #5 Member   Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2 YEAH...proceed please August 23rd, 2018, 05:13 AM #6 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2203 You need values of x + 45$^\circ\!$ between 45$^\circ\!$ and 405$^\circ\!$, so choose all integer values of k such that ±65.9$^\circ\!$ + k(180$^\circ\!$) is within that range, then you can get the desired (approximate) answers by subtraction of 45$^\circ\!$. For example, using -65.9 and k = 1 would lead to (-65.9 + 180 - 45)$^\circ\!$, which is 69.1$^\circ\!$. Tags identities, trigonometry Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Monokuro Trigonometry 1 May 13th, 2014 01:38 PM Monokuro Trigonometry 1 May 11th, 2014 07:05 AM tiba Trigonometry 5 May 24th, 2012 07:11 AM hoyy1kolko Algebra 2 March 2nd, 2011 10:49 PM hoyy1kolko Algebra 2 February 26th, 2011 12:43 AM

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