if 0°< A and B< 90° such that cosA =5/13 and sin B =4/5 , then find sin(A+B).
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cosA = 5/13
As we Know 5, 12, 13 a Triplet
Hence,
sinA = 12/13
As √1 - cos²A = sinA
sinB = 4/5
As we Know that 3, 4, 5 is Triplet
√1 - sin²B = cosB
Hence,
cosB = 3/5
We Know,
sin(A+B) = sinAcosB + cosAsinB
= 12/13 × 3/5 + 5/13 × 4/5
= 36/65 + 20/65
= ( 36 + 20 ) / 65
= 56/65.
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