$\sin{4} \theta = \cos{3} \theta + \sin{2} \theta$ হলে   $\theta$ এর মান নিচের কোনটি?

দেওয়া আ

$\begin{aligned} & \sin 4 \theta-\sin 2 \theta=\cos 3 \theta \\ \Rightarrow & 2 \sin \frac{2 \theta}{2} \cos \frac{6 \theta}{2}=\cos 3 \theta \\ \Rightarrow & 2 \sin \theta \cos 3 \theta=\cos 3 \theta \\ \Rightarrow & 2 \sin \theta \cos 3 \theta-\cos 3 \theta=0 \\ \Rightarrow & (\cos 3 \theta)(2 \sin \theta-1)=0\end{aligned}$

$\begin{array}{l}\text { if, } \cos 3 \theta=0 \\ \Rightarrow \cos 3\theta =\cos \frac{\pi}{2} \\ \Rightarrow 3\theta =2 n \pi \pm \pi / 2 \\ \theta=\frac{2n\pi}{3} \pm \frac{\pi}{6}\\ \text { If, } \\ 2 \sin \theta-1=0 \\ \Rightarrow \sin \theta=\frac{1}{2}=\sin \frac{\pi}{6} \\ \therefore \theta=\frac{2 n \pi}{3} \pm \frac{\pi}{6} \\ \therefore \theta=n \pi \pm(-1)^{n} \cdot \frac{\pi}{6} ; n \in \mathbb{Z} \\ n \in Z \\\end{array}$