November 15th, 2016, 08:34 AM  #1 
Newbie Joined: Oct 2015 From: huddersfield Posts: 16 Thanks: 1  Trigonometric identities
Can anyone please help me with this question? Solve the following between the angles of 0 and 360 deg 4cot²x  6 cosec x = 6 Last edited by skipjack; November 16th, 2016 at 05:35 AM. 
November 15th, 2016, 09:25 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,738 Thanks: 1388 
note the identity ... $\cot^2{x} = \csc^2{x}  1$ substitute $\csc^2{x}  1$ for $\cot^2{x}$ and solve the resulting quadratic ... 
November 16th, 2016, 04:51 AM  #3 
Newbie Joined: Oct 2015 From: huddersfield Posts: 16 Thanks: 1 
Can you show me the first stages of substituting the identity? I understand how to solve the quadratic and also getting the angles between 0 and 360, but I do not understand how to substitute the identity.
Last edited by skipjack; November 17th, 2016 at 04:56 AM. 
November 16th, 2016, 05:07 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,738 Thanks: 1388 
$4\cot^2{x}6\csc{x}=6$ substitute ... $4(\csc^2{x}1)6\csc{x}=6$ now, proceed ... 
November 24th, 2016, 11:21 AM  #5 
Newbie Joined: Nov 2016 From: Canada Posts: 13 Thanks: 3 Math Focus: All 
Roots of the equation are cosec x = 1/2 & cosec x = 1 Therefore sin x = 2 & sin x =1 sin x = 2: no solution, because sin x belongs to [1, 1] sin x = 1 => x = n*PI + (1)power of n * PI/2 for all values on n belongs to Z 
November 24th, 2016, 08:17 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 18,841 Thanks: 1564 
It's simpler to state that sin x = 1 implies x = $\pi$/2 + 2n$\pi$, where n is an integer.


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