Question

minimum value of cos 2x + cosx for all real value of x=

Answer 1

Answer:

$-\frac{9}{8}$

Step-by-step explanation:

Let y = cosx + cos2x

Now, we will expand cos2x using double angle rule:

$y=cosx+2cos^2x-1\\\\y=2(cos^2x+\frac{1}{2} cosx)-1\\\\y=2(cos^2x+2cosx*\frac{1}{4}+\frac{1}{16} -\frac{1}{16})-1\\\\y=2(cosx+\frac{1}{4} )^2-\frac{1}{8} -1\\\\\y=2(cosx+\frac{1}{4} )^2-\frac{9}{8}$

Therefore, the minimum value is $-\frac{9}{8}$