(D) Given $\sin \left(5 x+\frac{\pi}{4}\right)=0$.We know that $\sin \theta = 0$ implies $\theta = n\pi$ for any integer $n \in \mathbb{Z}$.Therefore,

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$\frac{-\pi}{20}+\frac{\pi}{5} n, n \in \mathbb{Z}$

(D) Given $\sin \left(5 x+\frac{\pi}{4}\right)=0$.We know that $\sin \theta = 0$ implies $\theta = n\pi$ for any integer $n \in \mathbb{Z}$.Therefore,$5x + \frac{\pi}{4} = n\pi$.Subtracting $\frac{\pi}{4}$ from both sides,we get $5x = n\pi - \frac{\pi}{4}$.Dividing by $5$,we get $x = \frac{n\pi}{5} - \frac{\pi}{20}$.Thus,$x = \frac{-\pi}{20} + \frac{n\pi}{5}$ for $n \in \mathbb{Z}$.

Class 11 Mathematics Trigonometrical Equations Solution of trigonometrical equations

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If $\sin \left(5 x+\frac{\pi}{4}\right)=0$,then $x$ is equal to

AP EAMCET 2021 All AP EAMCET

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$\frac{-\pi}{20}+\frac{\pi}{2} n, n \in \mathbb{Z}$
B
$\frac{\pi}{20}+\frac{\pi}{5} n, n \in \mathbb{Z}$
C
$\frac{-\pi}{5}+\frac{\pi}{5} n, n \in \mathbb{Z}$
D
$\frac{-\pi}{20}+\frac{\pi}{5} n, n \in \mathbb{Z}$

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