Докажите тождество ctg(70)-sqrt(3)=-4cos(70)

 [latex]ctg 70^\circ - \sqrt{3} =-4cos70^\circ [/latex] [latex]ctg70^\circ -ctg30^\circ =-4cos70^\circ [/latex] [latex] \frac{sin(30^\circ -70^\circ )}{sin70^\circ sin30^\circ } =-4cos70^\circ [/latex] [latex] \frac{-sin40^\circ }{sin70* \frac{1}{2} }=-4 cos70^\circ [/latex] [latex] \frac{-2sin40^\circ }{sin70^\circ } =-4cos70^\circ [/latex] [latex] \frac{-2*2sin20^\circ cos20^\circ }{sin(90^\circ -20^\circ )} =-4cos70^\circ [/latex] [latex] \frac{-4sin20^\circ cos20^\circ }{cos20^\circ } =-4cos70^\circ [/latex] [latex]-4sin20^\circ =-4cos70^\circ [/latex] [latex]-4sin(90^\circ -70^\circ )=-4cos70^\circ [/latex] [latex]-4cos70^\circ =-4cos70^\circ [/latex] что и требовалось доказать