pembuktian (sin²x + cos ²x) = 1 -2 sinx . cos x

kayanya ada salah tulis itu, sebab
[tex] {sin}^{2} (x) + {cos}^{2} (x) = 1[/tex]
tapi bila ditulis
[tex] {( \sin(x) - \cos(x) ) }^{2} = 1 - 2 \sin(x) \cos(x) ) [/tex]
bisa dibuktikan, langkahnya :

ingat bahwa :
[tex] {( a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab[/tex]
sehingga :
[tex] {( \sin(x) - \cos(x) ) }^{2} = 1 - 2 \sin(x) \cos(x) \\ { \sin(x) }^{2} + { \cos(x) }^{2} - 2 \sin(x) \cos(x) = 1 - 2 \sin(x) \cos(x) \\ [/tex]
ingat bahwa :
[tex] { \sin(x) }^{2} + { \cos(x) }^{2} = 1[/tex]
sehingga :
[tex] { \sin(x) }^{2} + { \cos(x) }^{2} - 2 \sin(x) \cos(x) = 1 - 2 \sin(x) \cos(x) \\ 1 - 2 \sin(x) \cos(x) = 1 - 2 \sin(x) \cos(x) \\ (terbukti)[/tex]