Question 1031206
.
Determine cos2x if sin^(4)x = 25/36 when 0 < x < &#960;/2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
If  {{{sin^4(x)}}} = {{{25/36}}},  then  {{{sin^2(x)}}} = {{{5/6}}}  and 

{{{cos(2x)}}} = {{{cos^2(x) - sin^2(x)}}} = {{{(1-sin^2(x)) - sin^2(x)}}} = {{{1 - 2*sin^2(x)}}} = {{{1 - 2*(5/6)}}} = {{{1 - 5/3}}} = {{{-2/3}}}.


The info 0 < x < {{{pi/2}}}  is irrelevant.
It is not used in the solution, and the solution/the answer does not depend on this condition.
</pre>