If sinA = 4/5 And cosB = 5/13, where 0 <A, B < π/2, find the values of the following:

(i) sin(A +B)

(ii) cos(A +B)

(iii) sin(A –B)

(iv) cos(A -B)

Given sinA = 4/5 And cosB = 5/13

We know that where 0 <A,B < π/2

Then,

(i) Sin(A +B)

__We know that sin(A +B) = sinA cosB + cosA sinB__

(ii) Cos(A +B)

__We know that cos(A +B) = cosA cosB__ __-__ __sinA sinB__

(iii) Sin(A –B)

__We know that sin(A -B) = sinA cosB - cosA sinB__

(iv) Cos(A –B)

__We know that cos(A -B) = cosA cosB__ __+__ __sinA sinB__

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