Given if $\sin2\theta$ = $2\sin\theta$, what would be the value of $\theta(\mathrm{principal})$. I asked my elder and he used $\sin2\theta=2\sin\theta\cos\theta$, I don't understand this now (nor do I want to), is there any other method? I am not that specialised in this field. Please keep it the minimal.
Help appreciated.
Best Answer
If you know that $\sin(2\theta)=2\sin\theta\cos\theta$ (and this is true no matter what number $\theta$ is) and that $\sin(2\theta)=\sin\theta$ (and this is true only for the particular numbers you're seeking), then you have $$ 2\sin\theta\cos\theta = 2\sin\theta. $$ You can divide by sides by $2\sin\theta$ unless $\sin\theta=0$. Then you get $$ \cos\theta = 1. $$ So either $\sin\theta=0$ or $\cos\theta=1$. But additionally, when $\cos\theta=1$ then in every case, $\sin\theta=0$, so it's redundant to add $\sin\theta=0$.
So you just need to find values of $\theta$ for which $\cos\theta=1$.