trigonometry

(sin a)² + (cos a)²= 1

(-4/5 )² + (cos a)² = 1

\({\cos a = \sqrt{1-(-\frac{4}{5})^2}=\sqrt{1-\frac{16}{25}}=\sqrt{\frac9{25}}=\frac35}\)
 

(sin b)² + (cos b)²= 1

(5/13)² + (cos b)² = 1

\({\cos b =\sqrt{1-(\frac{5}{13})^2} = \sqrt{1-\frac{25}{169}}=\sqrt{\frac{144}{169}}=\frac{12}{13} }\)

 

cos(a - b) = (cos a)(cos b) + (sin a)(sin b)

cos(a - b) = (3/5)(12/13)    + (-4/5)(5/13)

cos(a - b) = 36/65 - 4/13

cos(a - b) = 16/65