Trigonometry - Precalculus

Question

for positive acute angles A and B, it is known that tan A = 3/4 and sin B = 20/29. find the value of cos(A-B) in simplest form.

Answer 1

It was nice of the problem author to use two Pythagorean triples - 3, 4, 5 and 20, 21, 29

cos(a - b) = cos(a)cos(b) + sin(a)sin(b) = 4/5*21/29 + 3/5*20/29 = 144/145

Easy to check the answer

=COS(ATAN(3/4)-ASIN(20/29))

To see the fraction, either express as a fraction or multiply by 145 to get 144.