Đáp án:
$\dfrac{-32+255\sqrt{3}}{514}$
Giải thích các bước giải:
$\sin^2a+\cos^2a=1\Rightarrow \cos^2a=1-\sin^2a=1-\left (\dfrac{255}{257} \right )^2=\dfrac{1024}{66049}\\
\Rightarrow \cos a=\pm \dfrac{32}{257}$
Do $\dfrac{\pi}{2}<a<\pi\Rightarrow \cos a<0$
$\Rightarrow \cos a=\dfrac{-32}{257}\\
\cos (a-60^{\circ})=\cos a\cos 60^{\circ}+\sin a\sin60^{\circ}\\
=\dfrac{-32}{257}.\dfrac{1}{2}+\dfrac{255}{257}.\dfrac{\sqrt{3}}{2}\\
=\dfrac{-16}{257}+\dfrac{255\sqrt{3}}{514}\\
=\dfrac{-32+255\sqrt{3}}{514}$
