Question

sin(x+pi/4)=root2cosx

Answer 1

\[\sin x \cos \frac{ \pi }{4 }+\cos x \sin \frac{ \pi }{ 4 }=\sqrt{2}\cos x\]\[\sin x*\frac{ 1 }{\sqrt{2}}+\cos x*\frac{ 1 }{\sqrt{2}}=\sqrt{2}\cos x\]
\[\sin x+\cos x=2\cos x,\sin x=\cos x,\tan x=1=\tan \frac{ \pi }{4 }=\tan \left( n \pi+\frac{ \pi }{ 4} \right)\]
\[x=n \pi+\frac{ \pi }{ 4 },n is an integer.\]