If sinA = 4/5 And cosB = 5/13, where 0

Question

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)

Philoid · Accepted Answer

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

We know that where 0

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