How can this be solved?
#sin(x/2) + cosx -1 = 0#
1 Answer
Explanation:
Use the half-angle formula for sine:
First, use this formula. Then, isolate the radical and square both sides of the equation. Lastly, create a quadratic out of
Solve for when each factor equals
Here's a unit circle to remind us of where these certain cosine values are:
So:
Lastly, since we squared both sides of the equation earlier, there is a possibility that new answers that don't actually work were added. That means that we have to test all the answers we got in the original problem:
Testing
The solution
The solution
All the solutions work. The final answers are: