Question

cosx=5/13 and sin y=3/5 what is the exact value of cos (x+y)?

Answer 1

cos(X+y) = cosx*cosy-sinx*siny

Answer 2

cos(x+y)=cosx.cosy-sinx.siny=5/13*3/5-12/13*4/5

Answer 3

cos x =5/13
hence sin x=12/13 (using sin^2x + cos^2 x=1)
sin y=3/5
cos y=4/5
cos (x+y)=cos x*cos y - sin x*sin y
=5/13 *4/5 - 12/14 *3/5
=20/65-36/65
=(20-36)/65
=-16/65