What is the simplified form of $\frac{2 \cos 40^\circ -1}{\sin 50^\circ}$? I just encountered the following multiple choice question on a exam. It looks simple but surprisingly I couldn't decipher it! So I decided to mention it here. :)

What is the simplified form of $\dfrac{2 \cos 40^\circ -1}{\sin 50^\circ}$?  
  
  
*
  
*$4 \sin 10^\circ$  
  
*$4 \cos 10^\circ $  
  
*$-4 \sin 10^\circ$  
  
*$-4 \cos 10^\circ$
  

Any hint or help is appreciated. :)

Consider
$$
2\sin50^\circ\sin10^\circ=\cos(50^\circ-10^\circ)-\cos(50^\circ+10^\circ)
$$
