Question

Sin 30°+корень из 6cos45°sin60°-tg30°ctg150°+ctg45°

Answer 1

1/2+√6*√3/2*√2/2-1/√3*(-√3)+1=1/2+√6*√6/2+3+1=1/2+3+3+1=7,5

Answer 2

To calculate the given expression, we'll use the trigonometric identities for sine, cosine, and tangent of common angles.

Recall the following trigonometric identities:

1. sin(30°) = 0.5
2. cos(45°) = √2 / 2
3. sin(60°) = √3 / 2
4. tan(30°) = 1 / √3
5. cot(150°) = -√3
6. cot(45°) = 1

Now, let's evaluate the expression step by step:

Sin 30° + √6 cos 45° sin 60° - tan 30° cot 150° + cot 45°

1. sin 30° = 0.5
2. cos 45° = √2 / 2
3. sin 60° = √3 / 2
4. tan 30° = 1 / √3
5. cot 150° = -√3
6. cot 45° = 1

Now, let's substitute the values:

0.5 + √6 * (√2 / 2) * (√3 / 2) - (1 / √3) * (-√3) + 1

Now, simplify each term:

1. √6 * (√2 / 2) * (√3 / 2) = (√6 * √2 * √3) / 4 = (√12 * √3) / 4 = √36 / 4 = √9 / 2 = 3 / 2

2. (1 / √3) * (-√3) = -1

Substitute the simplified values back into the expression:

0.5 + 3/2 - 1 + 1

Now, add the numbers together:

0.5 + 3/2 - 1 + 1 = 0.5 + 1.5 = 2

So, the final result of the expression is 2.