Come si semplifica #Sin (pi / 6 + x) #?

Using the appropriate#color(blue)" Addition formula "#

#color(red)(|bar(ul(color(white)(a/a)color(black)(sin(A±B)sinAcosB±cosAsinB)color(white)(a/a)|)))#

then #sin(pi/6+x)=sin(pi/6)cosx+cos(pi/6)sinx#

Using the#color(blue)" exact value triangle ""for this angle"#

Then #sin(pi/6)=1/2" and " cos(pi/6)=sqrt3/2#

#rArrsin(pi/6+x)=1/2cosx+sqrt3/2sinx#