find the exact value of cos(a+b) under the given conditions

Question

sin a=7/25,pi/2<a<pi; cos b=2/5, 0<B<pi/2

Answer 1

Need to use the cosine angle sum formula:

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

a is in Q II and b is in Q1, so need to adjust signs accordingly

cos(a) = -√(25²-7²)/25 = -24/25

sin(b) = √5²-2²)/5 = 4.58/5

Then it is just a matter of substituting all the sine and cosine values into to the cos(a+b) formula.