Question 737717
sin(sin^-1(5/13)+cos^-1(3/5)) 
 let A = sin^-1(5/13) and B = cos^-1(3/5). 
 sin^-1(5/13), => sinA = 5/13 and  cos^-1(3/5) => cosB = 3/5. 
 sinA and cosB are positive  
 sinA = sqrt{1 - cos^2A} 
 sinA = sqrt{1 - (5/13)^2} 
 sinA = sqrt{1 - 25/169} 
 sinA = sqrt{144/169} 
 sinA = 12/13 
  
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 cosB = sqrt{1 - sin^2B} 
 cosB = sqrt{1 - (3/5)^2} 

 cosB = sqrt{1 - 9/25} 
 cosB = sqrt{16/25} 
 cosB = 4/5 
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sin(A + B) = sinA cosB + cosAsinB 
 (sin^-1(5/13)+cos^-1(3/5)) = 
 sinA = 12/13 
 cosB = 4/5 
 cosA = 3/5 
 sinB = 5/13. 
 (12/13 )*( 4/5) +(3/5)* (5/13 )
 12/13 * 4/5 = 48/65 
 3/5 *5/13 = 15/65 
 We get 
 48/65 + 15/65 = 63/65