Question

sin225°•cos480°•tg(-330°) •ctg(-240°)
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Answer 1

Ответ: -√2/12

Пошаговое объяснение:

sin(225)=sin (180+45)=-sin45= -√2/2

cos480=(cos360+120)=cos120=cos(180-60)=-cos60=-0.5

tg(-330)=tg(-360+30)=tg30=1/√3

ctg(-240)= ctg(-360+120)= ctg(120)=ctg(180-60)=-ctg(60)= -1/√3

=>sin225°•cos480°•tg(-330°) •ctg(-240°) =-√2/2*(-0.5)*(1/√3)*(-1/√3)=

=-√2/(4*3)= -√2/12

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Answer 2

sin(225°)=sin(π + 45°)=-sin45°=-(√2/2)

cos(480°)=cos(5π/2 + 30°)=-sin30°=-(1/2)

tg(-330°)=-tg(3π/2 + 60°)=-(-ctg60°)=√3/3

ctg(-240°)=-ctg(π+60°)=-ctg60°=-(√3/3)

(-(√2/2)) × (-(1/2) × √3/3 × (-(√3/3) =

- (√2 × 1 × √3 × √3)/(2 × 2 × 3 × 3)=-((3√2)/36)=-(√2/12).

ответ: -(√2/12).