Question

How do you use the half angle formulas to simplify the expression `-sqrt((1-cos(x-1))/2)`?

Answer 1

`-sqrt((1-cos(x-1))/2)=-sin((x-1)/2)`

Explanation:

We can use the half angle identity `cosA=1-2sin^2(A/2)`

Hence `-sqrt((1-cos(x-1))/2`

= `-sqrt((1-(1-2sin^2((x-1)/2)))/2)`

= `-sqrt(((2sin^2((x-1)/2)))/2)`

= `-sqrt(sin^2((x-1)/2))`

= `-sin((x-1)/2)`