Question

Find each exact value if 0 < x < pi/2 and 0 < y < pi/2 .

Answer 1

1. cos (x + y) if sin x = 5/13 and sin y = 4/5
2. sin (x – y) if cos x = 8/17 and cos y = 3/5
3. tan (x – y) if csc x = 13/5 and cot y = 4/3

Answer 2

In first case, you are to find cosx and cosy..

Answer 3

Using the identity :

\[\cos^2(x) + \sin^2(x) = 1\]

Answer 4

Then after finding you are supposed to use :

\[\cos(x+y) = \cos(x) \cos(y) - \sin(x) \sin(y)\]

Answer 5

Thanks for the method. I wasn't sure what I was supposed to use here.

Answer 6

Must remember for the intervals you are given with..

x and y are in 0 to 90 interval, and all trigonometric ratios in this range will be positive..

Answer 7

Just try once...