I recognize that as the cosine double angle formula. The cosine sum angle formula is
[tex]\cos (a+b) = \cos a \cos b - \sin a \sin b[/tex]
Setting a=b
[tex]\cos(2a) = \cos^2 a - \sin^2 a[/tex]
Substituting [tex]\cos^2 a = 1- \sin^2 a[/tex]
[tex]\cos(2a) = 1 - \sin ^2 a - \sin^2a = 1 - 2 \sin^2 a[/tex]
Setting a=x/2,
[tex]\cos x = 1 - \sin ^2 \frac x 2[/tex]
Answer: cos
