Question

Se sen a = 1/5 e cos b = 1/4, sendo a e b arcos do 1° quadrante, determine sem (a-b)

Answer 1

$sen{(a+b)}=sena.cosb+senb.cosa\\sen(a+b)=\frac{1}{5}.\frac{1}{4}+\frac{2\sqrt{6}}{5}.\frac{\sqrt{15}}{4}\\sen(a+b)=\frac{1}{20}+\frac{2.3\sqrt{10}}{20}=\frac{1-6\sqrt{10}}{20}$