Explanation:

\(\displaystyle{\cos{{\left(-{60}^{\circ}\right)}}}\)

first convert \(\displaystyle{60}^{\circ}\) in radians just for the sake of convenience of problem solving in trigonometry. since \(\displaystyle\pi\ \text{ radian }\ ={180}^{\circ}\Rightarrow{60}^{\circ}={\left({\frac{{\pi}}{{{3}}}}\right)}\ \text{ radians}\)

now, since \(\displaystyle{\cos{{\left(-\theta\right)}}}={\cos{\theta}}.\)

so, \(\displaystyle{\cos{{\left(-{\frac{{\pi}}{{{3}}}}\right)}}}={\cos{{\left({\frac{{\pi}}{{{3}}}}\right)}}}={\frac{{{1}}}{{{2}}}}\) (a standard value and should be memorised)

\(\displaystyle{\cos{{\left(-{60}^{\circ}\right)}}}\)

first convert \(\displaystyle{60}^{\circ}\) in radians just for the sake of convenience of problem solving in trigonometry. since \(\displaystyle\pi\ \text{ radian }\ ={180}^{\circ}\Rightarrow{60}^{\circ}={\left({\frac{{\pi}}{{{3}}}}\right)}\ \text{ radians}\)

now, since \(\displaystyle{\cos{{\left(-\theta\right)}}}={\cos{\theta}}.\)

so, \(\displaystyle{\cos{{\left(-{\frac{{\pi}}{{{3}}}}\right)}}}={\cos{{\left({\frac{{\pi}}{{{3}}}}\right)}}}={\frac{{{1}}}{{{2}}}}\) (a standard value and should be memorised)