Question

(1+sin 30°+sin 60°)(3 cos 60°- sin 60°)

Answer 1

Решение на фотографии

Answer 2

Let's calculate the expression step by step:

First, let's simplify the expression inside the first set of parentheses:

1 + sin 30° + sin 60°

Using trigonometric identities, we know that sin 30° = 0.5 and sin 60° = √3/2. Substituting these values into the expression:

1 + 0.5 + √3/2

Combining the terms:

1.5 + √3/2

Now, let's simplify the expression inside the second set of parentheses:

3 cos 60° - sin 60°

Using trigonometric identities, we know that cos 60° = 0.5 and sin 60° = √3/2. Substituting these values into the expression:

3 * 0.5 - √3/2

Combining the terms:

1.5 - √3/2

Now, let's multiply the two simplified expressions together:

(1.5 + √3/2)(1.5 - √3/2)

Using the difference of squares formula, (a + b)(a - b) = a^2 - b^2, we can simplify further:

(1.5)^2 - (√3/2)^2

1.5^2 is equal to 2.25, and (√3/2)^2 is equal to 3/4:

2.25 - 3/4

To subtract these fractions, we need a common denominator. Multiplying the numerator and denominator of 3/4 by 4:

2.25 - (3 * 4)/(4 * 4)

Simplifying the fraction:

2.25 - 12/16

The fraction 12/16 can be simplified by dividing both the numerator and denominator by 4:

2.25 - 3/4

Now, we have a common denominator of 4:

(2.25 * 4)/4 - 3/4

Multiplying the numerator:

9/4 - 3/4

Subtracting the fractions:

6/4

Simplifying the fraction:

3/2

Therefore, the expression (1 + sin 30° + sin 60°)(3 cos 60° - sin 60°) simplifies to 3/2 or 1.5.