Question 1122857
.
<pre>
{{{sin^4(2theta)}}} - {{{2 sin^2(2theta)}}} = -1  <====>  (is equivalent to) 


{{{sin^4(2theta) - 2*sin^2(2theta) + 1}}} = 0  <====>  (is equivalent to)


{{{(sin^2(2theta) -1)^2}}} = 0  <====>  (is equivalent to)


{{{sin^2(2theta)-1}}} = 0  <====>  (is equivalent to) 


{{{sin^2(2theta)}}} = 1   <====>  (is equivalent to)


{{{sin(2theta)}}} = +/- 1.


    Case 1.  {{{sin(2theta)}}} = 1   is equivalent to  {{{2theta}}} = {{{pi/2}}}, {{{pi/2 +- 2pi}}}, {{{pi/2 +- 4pi}}}, . . . , {{{pi/2 +- 2n*pi}}},  where n is any integer.

             General solution for this case is  {{{theta}}} = {{{pi/4 + n*pi}}},  where n is any integer.



    Case 2.  {{{sin(2theta)}}} = -1   is equivalent to  {{{2theta}}} = {{{(3pi)/2}}}, {{{(3pi)/2 +- 2pi}}}, {{{(5pi)/2 +- 4pi}}}, . . . , {{{(3pi)/2 +- 2n*pi}}},  where n is any integer.

             General solution for this case is  {{{theta}}} = {{{(3pi)/4 + n*pi}}},  where n is any integer



<U>Answer</U>.  Any angle of the set  {{{pi/4+k*pi}}}, {{{(3pi)/4+k*pi}}}  is the solution, where k is any integer.
</pre>

====================


One and only one question per post, PLEASE.


It is the policy, the rule and the requirement of this forum.