Question

1)sin(p/4-x)
2)sin(p/6+y)
3)cos(p/3-x)
4)tg(p/4-x)

Answer 1

1)sin(π/4-x)=sin(π/4)cosx-sinxcos(π/4)=(√2/2)cosx-sinx*√2/2=(√2/2)(cosx-sinx)
2)sin(π/6+y)=sin(π/6)cosx+sinxcos(π/6)=(1/2)cosx+sinx*(√3/2)(1/2)cosx+(√3/2)sinx
3)cos(π/3-x)=cos(π/3)cosx+sin(π/3)sinx=(1/2)cosx+(√3/2)sinx
4)tg(π/4-x) =(tg(π/4)-tgx)/(1+tg(π/4)tgx)=(1-tgx)/(1+tgx)
или если записать иначе
$tg( pi /4-x)= frac{tg( pi /4)-tgx}{1+tg( pi /4)tgx}= frac{1-tgx}{1+tgx}$