Sketching A Graph Using Differentiation

[themadhatter1]

Homework Statement

Homework Equations

The Attempt at a Solution

I don't understand how they get from step 4 to step 5. Wouldn't you factor a cos x out of the brackets then have $$(\cos x)(1-\frac{1}{6})$$ to the left of the brackets. Then you can multiply the $$(1-\frac{1}{6})$$ inside the brackets.However that would yield $$[\frac{5}{6}+\frac{10}{3}\sin^2x]$$ I don't understand how they are getting 1- (1/6) times the stuff inside the brackets.

 

[Coto]

$$\cos x - \frac{1}{6}[(1-2\sin^2 x)\cos x - 2\sin^2 x\cos x]$$

$$= \cos x - \frac{1}{6}[ \cos x (1-2\sin^2 x - 2\sin^2 x) ]$$

$$= \cos x - \frac{1}{6} \cos x(1-2\sin^2 x - 2\sin^2 x)$$

$$= \cos x [ 1 - \frac{1}{6}(1-2\sin^2 x - 2\sin^2 x) ]$$