Question

Answer 1

\(sin\left(2x+\dfrac{\pi}{4}\right)=1\)

\(\Leftrightarrow2x+\dfrac{\pi}{4}=\dfrac{\pi}{2}+k2\pi\left(k\in Z\right)\)

\(\Leftrightarrow x=\dfrac{\pi}{8}+k\pi\left(k\in Z\right)\)

\(x\in\left(0,2\pi\right)\)

\(S=\left\{\dfrac{\pi}{8},\dfrac{9\pi}{8}\right\}\)

Answer 2

\(cosx=sinx\)

\(\Leftrightarrow sinx-cosx=0\)

\(\Leftrightarrow sin\left(x-\dfrac{\pi}{4}\right)=0\)

\(\Leftrightarrow x-\dfrac{\pi}{4}=k\pi\)

\(\Leftrightarrow x=\dfrac{\pi}{4}+k\pi\left(k\in Z\right)\)

Vì : \(x\in\left(\dfrac{-\pi}{2},\dfrac{\pi}{2}\right)\)

\(S=\left\{\dfrac{\pi}{4}\right\}\)