Sometimes, we need to solve an equation like this:

This is a transformed equation and it is a very common type of problem. There is a very common mistake which I find students make which I want to make you aware of so you can solve these equations confidently every time. Let's see some examples!

Solve the equations:

1. $$\sin (x+30)=\frac{3}{4},0^{\circ }\le x\le {360}^{\circ }$$
2. $$\cos (5x)=\frac{\sqrt{3}}{2},0\le x\le 2\pi$$
3. $$\tan (2\theta -\frac{\pi }{5})=3,-\pi \le \theta \le \pi$$