ze zbior zadaań do kl 1 liceum Kurczaba, Świda  str 132 8.45 Oblicz: a) 4 * cos60 * sin 30 - cos30 * sin 60 b) ctg30 * ctg45 / (ctg60 * tg45) c) 18 * sin30 * tg 30 /(cos30 * tg60) d) 6 * (sin 30 * cos45 * ctg60) / (ctg30 * sin45)  

4*cos60*sin30-cos30*sin60= 4*1/2*1/2-pierw z3/2*pierw z 3/2= 4-pierw z9/4= 4-3/4= 9/4   ctg30*ctg45/(ctg60*tg60)= pierw z 3*1/(pierw z 3/3*pierw z 3/1)= pierw z 3/pierw z9/3= pierw z 3*3/3=pierw z 3*1=pierw z3   18*sin30*tg30/(cos30*tg60)= 18*1/2*pierw z3/3 / pierw z3/2*pierw z3= 9*pierw z3/3 / pierw z9/2= 9*pierw z3/3*2/3= 9*3/9=3     6*(sin30*cos45*ctg60)/(ctg30*sin45)= 6*(1/2*pierw z2/2*pierw z3/3)/pierw z3*pierw z2/2= 6*(1/2*pierw z3/3)/pierw z3= 6*pierw z3/6 / pierw z3= pierw z3/pierw z3 =1

a) 4 * 1/2 * 1/2 - √3/2 * √3/2 = 1 - 3/4 = 1/4 b) √3 * 1 : (√3/3 * 1) = √3/1 * 3/√3 = 3 c) 18 * 1/2 * √3/3 * ( √3/2 * √3) = 9√3/3 : 3/2 = 3√3 * 2/3 = 6√3/3 = 2√3 d) 6 * (1/2 * √2/2 * √3/3) : (√3 * √2/2) = 6 * (√2/4 * √3/3) : √6/2 = 6 * √6/12 : √6/2 = √6/2 * 2/√6 = 1