sinus y cosinus

( (2n+(-1))^{(1/2)}/n )^{2}+( (n+(-1))/n )^{2}=1
conjetura
ángulo = (1/2)·( (2(n+(-1))+(-1))/(2n+(-1)) )·pi


( 3^{(1/2)}/2 )^{2}+( 1/2 )^{2}=1 & ( ángulo = ( 1/6 )·pi )
( 5^{(1/2)}/3 )^{2}+( 2/3 )^{2}=1 & ( ángulo = ( 3/10 )·pi )
( 7^{(1/2)}/4 )^{2}+( 3/4 )^{2}=1 & ( ángulo = ( 5/14 )·pi )
( 9^{(1/2)}/5 )^{2}+( 4/5 )^{2}=1 & ( ángulo = ( 7/18 )·pi )






( (2n+(-1))^{(1/2)}/n )^{2}+( (n+(-1))/n )^{2}+(-1)( n/n^{2} )=( (n+(-1))/n )


( 3^{(1/2)}/2 )^{2}+( 1/4 )+(-1)( 2/4 )=( 1/2 )
( 5^{(1/2)}/3 )^{2}+( 4/9 )+(-1)( 3/9 )=( 2/3 )
( 7^{(1/2)}/4 )^{2}+( 9/16 )+(-1)( 4/16 )=( 3/4 )
( 9^{(1/2)}/5 )^{2}+( 16/25 )+(-1)( 5/25 )=( 4/5 )


sin((n+1)x)=sin(nx)cos(x)+sin(x)cos(nx)
sin((n+1)x)=(sin(x)cos((n+(-1))x)+sin((n+(-1))x)cos(x))cos(x)+sin(x)cos(nx)
sin((n+1)x)=sin(x)cos(nx)+sin((n+(-1))x)(sin(x))^{2}+sin((n+(-1))x)cos(x)^{2}+sin(x)cos(nx)


sin((n+1)x)=2·sin(x)cos(nx)+sin((n+(-1))x)


cos((n+1)x)=cos(x)cos(nx)+(-1)sin(nx)sin(x)