Question

If SinA =4/5and CosB =5/13,where 0<A,B<£/2find the value of sin(a+b)
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Answer 1

Answer:

53/65

Step-by-step explanation:

SinA=4/5, CosA=√(1-Sin²A)=√(1-16/25)=√((25-16)/25)=√(9/25)=3/5

CosB=5/13, SinB=√(1-Cos²B)=√(1-25/169)=√(144/169)=12/13

From the identity,

Sin(A+B)=SinACosB+CosASinB

=(4/5)*(5/13)+(3/5)*(11/13)

=(20/65)+(33/65)=53/65