<s>[INST] 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?
 [/INST] $cos 25^\circ+ sin 25^\circ=k$
$\implies cos (45-20) + sin (45-20) =k$
$\implies cos 45\cdot cos 20+ sin 45\cdot sin 20 + sin45\cdot cos 20 -cos 45\cdot sin 20=k$
$2\cdot(\frac{1}{\sqrt2})cos 20^\circ=k$
$cos 20^\circ=k\cdot(\frac{\sqrt{2}}{2})$
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