Question
Evaluate $$\dfrac{2\cos 80^\circ-\sin 70^\circ}{\cos 70^\circ}$$
My Working
I tried converting $80^\circ$ to $2\cdot 40^\circ$ and $70^\circ$ to $30^\circ+40^\circ$. This led to
$$\frac{2\cos (2\cdot 40^\circ)-(\frac{\sqrt3}{2}\sin40^\circ+\frac12\cos40^\circ)}{\frac{\sqrt3}{2}\cos40^\circ-\frac12\sin40^\circ}$$
I do not know which double angle formula to use for $2\cos 80^\circ$, and how to simply the expression. Could someone please help? Thank you!