Question

SINUS, COSINUS, TANGENS, COTANGENS.

Oblicz:

a) 4 * cos 60st * sin 30st - cos 30st * sin 60st =

b) 18 * sin 30st * tg 30st : (cos 30st * tg 60st) =

c) 12 * (tg 60 st - cos 60 st) * ( tg 30st + cos 30st) =

d) ( sin 45st + ctg 45st) * (6 * sin 60st - ctg 30 st) =

e) (cos 45st - cos 30st) * (cos 45st + cos 30st) =

f) (3 sin 45st + tg 60st) * (3 sin 45st - tg 60st) =

g) 4 (ctg 45st + sin 60st) * (cos 30st + tg 45st ) =

h) 2 (tg 30st - sin 45st) * (cos 45st - ctg 60st) =

Answer 1

a)   4 * cos 60st * sin 30st - cos 30st * sin 60st = 4 * 1/2 * 1/2 - √3/2 * √3/2 = 2 * 1/2 - 3/4= -3/4 = -0,75

b)18 * sin 30st * tg 30st : (cos 30st * tg 60st) =18* 1/2 * √3/3 : (√3/2 * √3)=9 * √3/3 : 3/2=3√3 * 2/3= 2√3

c)12 * (tg 60 st - cos 60 st) * ( tg 30st + cos 30st) = 12* (√3-1/2)* (√3/3+√3/2)=12√3-6* (2√3/6+3√3/6)=12√3-2√3-3√3=7√3

d)( sin 45st + ctg 45st) * (6 * sin 60st - ctg 30 st) =(√2/2+1) * (6*√3/2-√3)=(√2/2+2/2)*(3√3-√3)=2√2/2 * 2√3=2√6

e)(cos 45st - cos 30st) * (cos 45st + cos 30st)= (√2/2-√3/2) * (√2/2+√3/2)= (√2/2)² - (√3/2)²=2/4-3/4=-1/4= -0,25

f)(3 sin 45st + tg 60st) * (3 sin 45st - tg 60st) = (3*√2/2+√3) * (3*√2/2-√3)=(3√2/2)²-√3²=9-3 = 6

g)4 (ctg 45st + sin 60st) * (cos 30st + tg 45st )=4(1+√3/2) * (√3/2+1)=2√3+4+3+2√3=4√3+7

h) 2 (tg 30st - sin 45st) * (cos 45st - ctg 60st) = 2(√3/3-√2/2) * (√2/2-√3/3)= √6/3-2/3-3/3+√6/3=√6-2-3+√6/3 (całe działanie nad 3)=2√6-5/3 ( również całe działanie.)