Question:
Find the general solution of each of the following equations:
sin x = tan x
Solution:
To Find: General solution.
Given: $\sin x=\tan x \Rightarrow \sin x=\sin x \div \cos x$
So $\sin x=0$ or $\cos x=1=\cos (0)$
Formula used: $\sin \theta=0 \Rightarrow \theta=n \pi, n \in \mid$ and $\cos \theta=\cos \alpha \Rightarrow \theta=2 k \pi \pm \alpha, k \in \mid$
$x=n \pi$ or $x=2 k \pi$ where $n, k \in l$
So general solution is $x=n \pi$ or $x=2 k \pi$ where $n, k \in \mid$