Question

1) sin 60° - 2cos 30° + tg 60°, 2) cos 30º. sin 60° + ctg 600-tg 60°3) 2 sin 30° - 2cos 30°. tg 30° - cos 0° sin 90°​

Answer 1

Ответ:

1) sin60°-2cos 30°+tg60°= √3/2 - 2 × √3/2 - √3= √3/2 - √3 - √3 = - 3√3/2≈-2,60

3)2sin 30° - 2cos30°.tg30°-cos0° sin90°= 2 × 1/2 - 2 × √3/2 × 1/√3 - 1 × 1 = 1 - 1 - 1=-1

2-ой пример там точно ctg 600?

Answer 2

1)  √3/2 - 2 × √3/2 - √3= √3/2 - √3 - √3 = - 3√3/2≈-2,60

2) 3/4 + ctg(600) -√3

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

Answer 3

Let's simplify each of these expressions step by step:

1. sin 60° - 2cos 30° + tg 60°

First, we'll find the values of sin 60°, cos 30°, and tg 60°:

sin 60° = √3/2 cos 30° = √3/2 tg 60° = √3

Now, plug these values into the expression:

√3/2 - 2(√3/2) + √3

Now, simplify:

(√3/2) - (2√3/2) + √3

Combine like terms:

(√3 - 2√3 + √3)/2

Now, simplify the numerator:

(√3 - 2√3 + √3) = (-√3)/2

So, the simplified expression is:

(-√3)/2

2. cos 30º. sin 60° + ctg 60° - tg 60°

First, find the values of cos 30°, sin 60°, and tg 60°:

cos 30° = √3/2 sin 60° = √3/2 tg 60° = √3

Now, plug these values into the expression:

(√3/2) * (√3/2) + (1/√3) - √3

Now, simplify:

(3/4) + (1/√3) - √3

To add these fractions, we need a common denominator, which is √3:

(3/4) + (√3/3) - (√3 * √3/√3) (Multiply the second fraction by √3/√3 to rationalize the denominator)

Now, simplify:

(3/4) + (√3/3) - (3/√3)

Now, find a common denominator, which is 12:

(9/12) + (4√3/12) - (12/12√3)

Now, add the fractions:

(9 + 4√3 - 12√3)/12

Combine like terms in the numerator:

(9 - 8√3)/12

So, the simplified expression is:

(9 - 8√3)/12

3. 2 sin 30° - 2cos 30° * tg 30° - cos 0° * sin 90°

Let's calculate each part separately:

sin 30° = 1/2 cos 30° = √3/2 tg 30° = sin 30° / cos 30° = (1/2) / (√3/2) = 1/√3 = √3/3 cos 0° = 1 sin 90° = 1

Now, plug these values into the expression:

2(1/2) - 2(√3/2)(√3/3) - (1 * 1)

Now, simplify:

1 - 2(√3/3) - 1

Combine like terms:

(1 - 1) - 2(√3/3)

Now, simplify further:

-2(√3/3)

So, the simplified expression is:

-2(√3/3)