Question 1196621
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If sin(x) = 1/3 and sec(y) = 13/12, where x and y lie between 0 and 𝜋/2,
evaluate the expression sin(x − y).
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<pre>
If sin(x) = 1/3 and x lies between 0 and 𝜋/2,  then  

   cos(x) = {{{sqrt(1-sin^2(x))}}} = {{{sqrt(1-(1/3)^2)}}} = {{{sqrt(8)/3}}}.


If sec(y) = 13/12,  then  

   cos(y) = {{{1/sec(y)}}} = 12/13  and  sin(y) = {{{sqrt(1-cos^2(y))}}} = {{{sqrt(1-(12/13)^2)}}} = {{{5/13}}}.


sin(x-y) = sin(x)*cos(y) - cos(x)*sin(y) = {{{(1/3)*(12/13) - (sqrt(8)/3)*(5/13)}}} = {{{(12-5*sqrt(8))/39}}} = 

         = {{{(12-5*2*sqrt(2))/39}}} = {{{(12-10*sqrt(2))/39}}}.        <U>ANSWER</U>
</pre>

Solved.