Question

4 sin^2 120°-3 cos 180°-3 ctg 135°

Answer 1

Ответ:10

Пошаговое объяснение:

4(V3/2)^2-3*(-1)-3(-1)=4*3/4+3+3=10

SIN120=SIN(180-60)=SIN60=v3/2,  CTG135=CTG(90+45)=-TG45=-1

Answer 2

To simplify the expression, let's first evaluate the trigonometric functions at the given angles:

1. sin(120°) = √3/2 (since sin(120°) = sin(180° - 60°) and sin(60°) = √3/2)
2. cos(180°) = -1 (cosine of 180° is -1)
3. ctg(135°) = 1/tan(135°) (cotangent is the reciprocal of tangent) tan(135°) = -1 (since tan(180° - 45°) = tan(45°) = 1) Therefore, ctg(135°) = 1/(-1) = -1

Now, substitute these values back into the expression:

4 sin^2 120° - 3 cos 180° - 3 ctg 135°

= 4 * (sin^2 120°) - 3 * cos 180° - 3 * ctg 135°

= 4 * ( (√3/2)^2 ) - 3 * (-1) - 3 * (-1)

= 4 * (3/4) - (-3) - (-3)

= 3 - (-3) - (-3)

= 3 + 3 + 3

= 9

Therefore, the simplified value of the expression is 9.