If cos42° + sin42° = k then what is the value of cos242° - sin242°.

cos²42° - sin²42° = (cos42° + sin42°)(cos42° - sin42°) = (k)(x)

If cos + sin = k, than cos - sin = \(\sqrt {2-k^2}\)  (Always)

So, cos²42° - sin²42° = k\(\sqrt {2-k^2}\)