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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