1. sin(x) + sqrt2 = - sinx
2. 3 tan(x/2)+3=0
3. solve for cosx ; cos x =1/2
Add to both sides, and subtract from both sides:
Now I'm not sure what sort of answer is needed now. Do you use a calculator to work out a single answer for , giving your answer in degrees? Or do you want lots of answers in radians, involving things like and ?
I don't know. But in degrees, possible answers include , , and so on.
Again, you have lots of possibilities now. One answer is that
There are lots of other possibilities...
By now, I'm guessing that you want all the possible values of if
I reckon the easiest way is to look at a sketch graph of , and work them out from that.
The first positive value is (or radians), but there's another on the other side of the y-axis, where ( )
The graph repeats every , or radians, so you get more answers by adding ( radians) on to these two answers. So in degrees:
I'll leave it to you to find these answers in radians, if you need to.