Question 1092330
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1.  Since sin(A) = {{{3/5}}},  cos(A) = {{{sqrt(1 - sin^2(A))}}} = {{{sqrt(1-(3/5)^2)}}} = {{{sqrt(1-9/25)}}} = {{{sqrt(25-9)/25)}}} = {{{sqrt(16/25)}}} = {{{4/5)}}}.


2.  Since cos(B) = {{{5/13}}},  sin(B) = {{{sqrt(1 - cos^2(B))}}} = {{{sqrt(1-(5/13)^2)}}} = {{{sqrt(1-25/169)}}} = {{{sqrt(169-25)/169)}}} = {{{sqrt(144/169)}}} = {{{12/13)}}}.


3.  Now sin(A+B) = sin(A)*cos(B) + cos(A)*sin(B) = {{{(3/5)*(5/13) + (4/5)*(12/13)}}} = {{{15/65 + 48/65}}} = {{{63/65}}}.
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<U>Answer</U>.  &nbsp;sin(A+B) = {{{63/65}}}.