If $\cos 25^\circ + \sin 25^\circ = k,$ then what is $\cos 20^\circ$? Question: 
If $$\cos 25^\circ + \sin 25^\circ = k,$$ then what is $\cos 20^\circ$?

What I did:
I tried to square both sides, and obtained that $\sin 50 = k^2 -1$, however, this didn't get me anywhere. Then I tried splitting 25 into 20 + 5 but that didn't get me anywhere either. Can someone just point me in the right direction?

Then we have 
$$k^2=(\cos 25^\circ + \sin 25^\circ)^2=1+2\cos 25^\circ \sin 25^\circ=1+\sin 50^\circ.$$
Note that $\cos 40^\circ=\cos(90^\circ-50^\circ)=\sin 50^\circ$. Hence,  we have 
$$\tag{1}\cos 40^\circ=k^2-1.$$
Now 
$$\tag{2}\cos 40^\circ=2\cos^2 20^\circ-1.$$
Now combining $(1)$ and $(2)$ gives you the answer. 
