Question

Given a and b are first quadrant angles, sin a=5/13 and cos b=3/5 evaluate cos (a+b)1) 56/652) 33/653) 16/65

Answer 1

`\begin{gathered} \sin \text{ a =}(5)/(13) \\ \cos b=(3)/(5) \\ \text{For find the value of cos a :} \\ \text{base}=\sqrt[]{13^2-5^2} \\ b=\sqrt[]{169-25} \\ b=\sqrt[]{144} \\ b=12 \\ \cos \text{ a =}(12)/(13) \\ F\in d\text{ the value of sin b:} \\ \text{perpendicular =}\sqrt[]{5^2-3^2} \\ p=\sqrt[]{25-9} \\ p=4 \\ \sin \text{ b =}(4)/(5) \\ \cos (a+b)\text{ = }cos\text{ a cos b-sin a sin b} \\ \cos (a+b)=\text{ }(12)/(13)*(3)/(5)-(5)/(13)*(4)/(5) \\ \cos (a+b)=(36)/(65)-(20)/(65) \\ \cos (a+b)=(16)/(65) \end{gathered}`