Question 1007411
Please help me solve this equation. I have a huge trig test tomorrow and I have no idea what I am doing... csc^2(2x)-csc(2x)=2
<pre>{{{csc^2 (2x) - csc (2x) = 2}}}
{{{1/(sin^2 (2x)) - 1/(sin (2x)) = 2}}} ------- Converting from csc to sin
{{{1 - sin (2x) = 2 sin^2 (2x)}}} ---------- Multiplying by LCD, {{{sin^2 (2x)}}}
{{{2 sin^2 (2x) + sin (2x) - 1 = 0}}}
[2 sin (2x) - 1][sin (2x) + 1] = 0 ------ Factoring trinomial
2 sin (2x) – 1 = 0	    AND		  sin (2x) + 1 = 0
2 sin (2x) = 1		    AND		  sin (2x) = 0 - 1
{{{sin (2x) = 1/2}}}	            AND           sin (2x) = - 1
{{{sin^(- 1)(1/2) = 2x}}}            AND   	  {{{sin^(- 1)(- 1) = 2x}}}
30 = 2x			    AND  	  270 = 2x 
{{{highlight_green(30/2 = x = 15^o = pi/12)}}} (Q I)	    AND          {{{highlight_green(270/2 = x = 135^o = 3pi/4)}}} (Q II)
{{{highlight_green(x = 165^0 = 11pi/12)}}} (Q II)      

No INTERVAL was stated (the likes of: {{{0^o <= x <= 360^0}}}) so these are the 3 solutions