Question

tgx+ctgx+tg3x+ctg3x=???

Answer 1

tgx+tg3x+ctgx+ctg 3x=tgx+tg3x+(tgx+tg3x)/tgxtg3x=(tgx+tg3x)(tgxtg3x+1)/tgxtg3x=(sin(x+3x)/cosxcos3x)*(sinx sin3x+cosx cos3x)*cosx cos3x/sinx sin3x=sin4x*cos2x/sinx sin3x=1/2*(sin2x+sin3x)/(1/2*(cos2x- cos4x))=sin(5x/2)cos( -x/2)/-sin3x sin(-x)=sin 5x/2 cos x/2 /sin3xsinx