Question 873142
<pre>
find the exact value of cos(a+B)
if sin a= -4/5, and sin B= 5/13

cos(a) = ±&#8730;<span style="text-decoration: overline">1-sinČ(a)</span> = {{{"" +- sqrt(1-(-4/5)^2)}}} = {{{"" +- sqrt(1-16/25))}}} = {{{"" +- sqrt(25/25-16/25))}}} = {{{"" +- sqrt(9/25))}}} = {{{"" +- 3/5)}}}

cos(B) = ±&#8730;<span style="text-decoration: overline">1-sinČ(B)</span> = {{{"" +- sqrt(1-(5/13)^2)}}} = {{{"" +- sqrt(1-25/169))}}} = {{{"" +- sqrt(169/169-25/169))}}} = {{{"" +- sqrt(144/169))}}} = {{{"" +- 12/13)}}} 

Case 1:  a is in Q3 and B is in Q1

cos(a+B) = cos(a)cos(B) - sin(a)sin(B) = (-3/5)(12/13) - (-4/5)(5/13) = -16/65

Case 2:  a is in Q3 and B is in Q2

cos(a+B) = cos(a)cos(B) - sin(a)sin(B) = (-3/5)(-12/13) - (-4/5)(5/13) = 56/65

Case 3:  a is in Q4 and B is in Q1

cos(a+B) = cos(a)cos(B) - sin(a)sin(B) = (3/5)(12/13) - (-4/5)(5/13) = 56/65

Case 4:  a is in Q4 and B is in Q2 

cos(a+B) = cos(a)cos(B) - sin(a)sin(B) = (3/5)(-12/13) - (-4/5)(5/13) = -16/65

Two possible solutions: -16/65 and 56/65

Edwin</pre>