Question

How do you use the half angle formulas to simplify the expression `sqrt((1+cos4x)/2)`?

Answer 1

`sqrt((1+cos4x)/2)=cos2x`

Explanation:

We use the identity `cosA=2cos^2(A/2)-1`

as such `cos4x=2cos^2((4x)/2)-1=2cos^2 2x-1`

Hence `sqrt((1+cos4x)/2)`

= `sqrt((1+2cos^2 2x-1)/2)`

= `sqrt(cos^2 2x)`

= `cos2x`