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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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