TRIG EXPRESSION value?

Question

Let cos alpha = (sqroot 5) / 5: 0 < alpha < pi/2; sin beta = -4/5: -pi/2 < beta < 0. Find the exact value of the following:

a) cos(alpha - beta)

b) tan(alpha + beta)

please help me and explain this to me, having a hard time, thanks!!

Answer 1

Here are some hints for part (a):

look up the formula for the cosine of the difference of two angles. You'll find that cos (alpha-beta) is an expression that involves each of the following:

cos alpha
sin alpha
cos beta
sin beta
You are given two of those, and by drawing right triangles in the appropriate quadrants you can get sin alpha and cos beta.

For part (b), look up the formula for tangent of a sum. From what you did in (a), you can determine tan alpha and tan beta since tangent is sine divided by cosine.