Question

Find all solutions in the interval [0, 2π).

cos x = sin x

Answer 1

\[\sin x= \cos x \rightarrow \sin ^{2} x= \cos ^{2} x \rightarrow \sin ^{2} x=(1-\sin ^{2} x) \rightarrow 2\sin ^{2} x=1 \rightarrow \sin x= \pm \frac{ \sqrt{2} }{ 2 }\]
\[x=\frac{ k \pi }{ 4 } \rightarrow \sin x=\cos x \rightarrow x=\frac{ \pi }{ 4 } and \frac{ 5 \pi }{ 4 }\]