Trigonometric Functions — Maths STD 12 Science — Question

$\therefore \sin \theta=\frac{\sin \theta}{\cos \theta}$

$\therefore \sin \theta \cos \theta=\sin \theta$

$\therefore \sin \theta \cos \theta-\sin \theta=0$

$\therefore \sin \theta(\cos \theta-1)=\theta$

$\therefore$ either $\sin \theta=0$ or $\cos \theta-1=0$

$\therefore$ either $\sin \theta=0$ or $\cos \theta=1$

$\therefore$ either $\sin \theta=0$ or $\cos \theta=\cos \theta \ldots[\because \cos 0=1]$

The general solution of sinθ = 0 is θ = nπ, n ∈ Z and cos θ = cos ∝ is θ = 2nπ ± ∝, where n ∈ Z.

∴ the required general solution is given by

$\theta=n \pi, n \in Z$ or $\theta=2 n \pi \pm 0, n \in Z$

$\therefore \theta=n \pi, n \in Z$ or $\theta=2 n \pi, n \in Z$