In Example 4, change cos 1/2x to sin 1/2x and on the right of the equal sign change the + to −.

Data from Example 4

Solve the equation cos(x/2) = 1 + cos x (0 ≤ x

By using the half-angle formula for cos (x/2) and then squaring both sides of the resulting equation, this equation can be solved:

|1 + cosx 2 1+ cosx 2 2 cosx+3 cos x + 1 = 0. H = 1 + cos.x 1 + 2 cosx + cosx (2cosx +1)(cosx + 1) = 0 cosx =--- = 2 4 -4, 3 3 X =