Question

cos(a/2) = ±√((1 + cosa)/2) for all values of a.
TRUE or FALSE

Answer 1

TRUE

Answer 2

identity:

\[\cos^2(a) = \frac{ 1 + \cos(2a) }{ 2 }\]

so:

\[\frac{ 1 + \cos(a) }{ 2 } = \cos^2 (a/2)\]

so we have:

we can move the plus-minus in front of the sqrt to the left side, and square rooting yields it's own plus-minus sign

\[\pm cos(a/2) = \pm \cos(a/2)\]

since cos is an even function

Answer 3

added random stuff lol and forgot to erase.

Answer 4

ignore the last sentence (about even function)