goniometria

cos(2x) = –1+2cos2(x) cos(3x) = –3cos(x)+4cos3(x) cos(4x) = 1–8cos2(x)+8cos4(x) cos(5x) = 5cos(x)–20cos3(x)+16cos5(x) cos(6x) = –1+18cos2(x)–48cos4(x)+32cos6(x) cos(7x) = –7cos(x)+56cos3(x)–112cos5(x)+64cos7(x) cos(8x) = 1–32cos2(x)+160cos4(x)–256cos6(x)+128cos8(x) cos(9x) = 9cos(x)–120cos3(x)+432cos5(x)–576cos7(x)+256cos9(x) cos(10x) = –1+50cos2(x)–400cos4(x)+1120cos6(x)–1280cos8(x)+512cos10(x)  

sin(2x) = 2cos(x) sin(x) sin(3x) = –sin3(x)+3cos2(x) sin(x) sin(4x) = –4cos x) sin3(x)+4cos3(x) sin(x) sin(5x) = sin5(x)–10cos2(x) sin3(x)+5cos4(x) sin(x) sin(6x) = 6cos(x) sin5(x)–20cos3(x) sin3(x)+6cos5(x) sin(x) sin(7x) = –sin7(x)+21cos2(x) sin5(x)–35cos4(x) sin3(x)+7cos6(x) sin(x) sin(8x) = –8cos(x) sin7(x)+56cos3(x) sin5(x)–56cos5(x) sin3(x)+8cos7(x) sin(x) sin(9x) = sin9(x)–36cos2(x) sin7(x)+126cos4(x) sin5(x)–84cos6(x) sin3(x)+9cos8(x) sin(x) sin(10x) = 10cos(x) sin9(x)–120cos3(x) sin7(x)+252cos5(x) sin5(x)–120cos7(x) sin3(x)+10cos9(x) sin(x)