How Do You Calculate cos(a-b) from Given Sine and Cosine Values?

[Michael_Light]

Homework Statement

Given that
sin(a) + cos(b) = 3^1/2/2 and
sin(a) + sin(b) = 3/2

Find cos(a-b)

Homework Equations

The Attempt at a Solution

Can anyone give me some hints?

 

[ehild]

See: http://file.glpacademy.co.kr/eTAP/mathfiles/english/trigo/lesson2/instructiontutor_last.html

ehild

 

[eumyang]

Try taking the Pythagorean identity
cos² b + sin² b = 1

and rewriting it in terms of sin a. I found an answer by starting this way, but it is a decimal approximation.

 

[Michael_Light]

The answer i get is 0.7858... but the answer given is 0.5. What answer do you guys get?

 

[eumyang]

0.7858... is what I got, too. Maybe there is a typo in the original problem or in the answer?

 

[I like Serena]

I get a total of 2 solutions: 0.2599 and 0.7858