Question

GPT: \(\sin\left(x-\dfrac{\pi}{4}\right)=\dfrac{\pi}{2}\)

Answer 1

\(\sin\left(x-\dfrac{\pi}{4}\right)=\dfrac{\pi}{2}\Leftrightarrow x-\dfrac{\pi}{4}=\dfrac{\pi}{2}+k2\pi\)

 

\(\Leftrightarrow x=\dfrac{3\pi}{4}+k2\pi\left(k\in Z\right)\)

Answer 2

`sin(x- (pi)/4) = (pi)/2`

`<=> x - (pi)/4 = (pi)/2 + k2(pi)`

`<=> x = (3(pi))/4 + k2(pi)`.