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If $\sin \left(5 x+\frac{\pi}{4}\right)=0$, then $x$ is equal to
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Verified Answer
The correct answer is:
$\frac{-\pi}{20}+\frac{\pi}{5} n(n \in z)$
$\sin \left(5 x+\frac{\pi}{4}\right)=0=\sin n \pi(\because \sin n \pi=0)$ where $n \in Z$
$$
\begin{array}{rlrl}
\Rightarrow & & 5 x+\frac{\pi}{4} & =n \pi \\
\Rightarrow & x & =\frac{1}{5}\left(n \pi-\frac{\pi}{4}\right)=\frac{n \pi}{5}-\frac{\pi}{20}
\end{array}
$$
$$
\begin{array}{rlrl}
\Rightarrow & & 5 x+\frac{\pi}{4} & =n \pi \\
\Rightarrow & x & =\frac{1}{5}\left(n \pi-\frac{\pi}{4}\right)=\frac{n \pi}{5}-\frac{\pi}{20}
\end{array}
$$
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