Question 1083906
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I will solve only one problem here, problem B).


<pre>
B. {{{cos(sin(-1)(x/5))}}}  is  {{{cos(arcsin(x/5))}}}.


   1.  Let {{{alpha}}} = {{{arcsin(x/5)}}}.

       Then {{{alpha}}} is the angle in Q1 (if x >= 0)  or in QVI (if x < 0).

       In any case,  {{{sin(alpha)}}} = {{{x/5}}} and {{{cos(alpha)}}} is positive.


   2.  Since  {{{sin(alpha)}}} = {{{x/5}}}, it implies that 

       {{{cos(alpha)}}} = {{{sqrt(1-sin^2(alpha))}}} = {{{sqrt(1 - (x/5)^2)}}} = {{{sqrt((25-x^2)/25)}}} = {{{(sqrt(25-x^2))/5}}}.


       So, it matches with #2).
</pre>

Actually, each of the rest cases is solved in a similar way.