Mathematics - Trigonometric Equation Question with Solution | TestHub

$\cos 7\theta =\cos \theta -\sin 4\theta$ $\Rightarrow \sin 4\theta =\cos \theta -\cos 7\theta$ $\Rightarrow \sin 4\theta =2\sin 4\theta \sin 3\theta$ $\Rightarrow \sin 4\theta (1-2\sin 3\theta )=0$ $\therefore \sin 4\theta =0$ or $\sin 3\theta =\frac{1}{2}$ $\Rightarrow 4\theta =n\pi$ or $3\theta =n\pi +(-1{)}^n\frac{\pi }{6}$ $\Rightarrow \theta =\frac{n\pi }{4}$ or $\frac{n\pi }{3}+(-1{)}^n\frac{\pi }{18}$