Question

Oblicz:
a) ctg 30 x ctg 45 : (ctg 60 x tg 45)
b) (3sin 45+ tg 60) x ( 3sin 45 - tg 60 )
c)12 x (tg 60-cos 60) x (tg30 + cos 30 )

Answer 1

Wartosci bierzesz z tabeli funkcji trygonometrycznych
ctg30 =√3
ctg45=1
ctg60= √3 / 3
sin45 =√2/2
tg60 =√3
cos60= 1/2
cos30= √3/2
tg30 =√3/3
a) ctg 30 * ctg 45 / (ctg 60 * tg 45) = √3 * 1 / ( (√3 / 3) * 1 ) =
= √3 / (√3 / 3) = 3
b) (3sin 45+ tg 60) * ( 3sin 45 - tg 60 ) = ( 3 * √2/2 + √3 )* (3 * √2/2 - √3 ) = ( 3√2/2 + √3 ) * (3√2/2 - √3 ) = 18/4 -3 = 4½ - 3= 1½
c) 12 * (tg 60-cos 60) * (tg30 + cos 30 ) = 12 * ( √3 - 1/2)*( √3/3 +√3/2 )= 12 * (1 + 3/2 - √3 /6 - √3 /4 ) =12 + 18 - 2√3 -3√3=
=30 -5√3

Answer 2

A) √3×1÷(√3/3×1)= √3÷√3/3=3

b)(3sin 45+ tg 60) x ( 3sin 45 - tg 60 )= (3sin45)²-(tg60)²= (3*√2/2)²-(√3)²= 4,5-3=1,5

c)12 x (tg 60-cos 60) x (tg30 + cos 30 )= 12*(√3-1/2)*(√3/3+√3/2)=
(12√3-6)*(√3/3+√3/2)= (12√3*√3/3)+(12√3*√3/2)-(-6*√3/3)-(-6*√3/2)=
12+18-2√3-3√3=30-5√3