Question

вычислите а) ( tg61-tg16)/1+tg61*tg16; б) cos85+cos35-cos25

Answer 1

$frac{tg61^{circ}-tg16^{circ}}{1+tg61^{circ}*tg16^{circ}}=tg(61^{circ}-16^{circ})=tg45^{circ}=1\\cos85^{circ}+cos35^{circ}-cos25^{circ}=2cos(frac{85^{circ}+35^{circ}}{2} )cos(frac{85^{circ}-35^{circ}}{2})-cos25^{circ}=\\2cos60^{circ}cos25^{circ}-cos25^{circ}=2*frac{1}{2}cos25^{circ}-cos25^{circ}=cos25^{circ}-cos25^{circ}=0$