a, b are angles in the first quadrant such that tan(a)=3/4 and tan(b) = 5/12
Find sin(a+b)
+128474 In the first case r =sqrt ( 3^2 + 4^2) = sqrt (25) = 5
So sin (a) = 3/5 cos ( a ) = 4/5
In the second case r = sqrt ( 5^2 + 12^2) = sqrt (169) =13
So sin (b) = 5/13 cos (b) = 12/17
sin (a + b) =
sin a cos b + sin b cos a =
(3/5) ( 12/17) + (5/13) (4/5) =
( 36 / 85 ) + (20 / 65) =
808 / 1105
