Question

4 tg(30°)-5 cos(30°)+6 sin(60°)-4cos(45°)-tg(60°)

Answer 1

4*√3/3-5*√3/2+6*√3/2-4*√2/2-√3=(8√3-15√3+18√3-6√3)/6-2√2=5√3/6-2√2

Answer 2

To calculate the value of the expression, let's evaluate each term one by one:

1. tg(30°): The tangent of 30 degrees is √3/3. Therefore, 4 tg(30°) = 4 * (√3/3) = 4√3/3.

2. cos(30°): The cosine of 30 degrees is √3/2. Therefore, 5 cos(30°) = 5 * (√3/2) = 5√3/2.

3. sin(60°): The sine of 60 degrees is √3/2. Therefore, 6 sin(60°) = 6 * (√3/2) = 3√3.

4. cos(45°): The cosine of 45 degrees is √2/2. Therefore, 4 cos(45°) = 4 * (√2/2) = 2√2.

5. tg(60°): The tangent of 60 degrees is √3. Therefore, tg(60°) = √3.

Now, let's substitute these values into the expression:

4 tg(30°) - 5 cos(30°) + 6 sin(60°) - 4 cos(45°) - tg(60°)

= 4√3/3 - 5√3/2 + 3√3 - 2√2 - √3

To simplify this expression, we need to find a common denominator for the fractions:

= (8√3 - 15√3 + 18√3 - 12√2 - 3√3) / 6

= (8√3 - 15√3 + 18√3 - 3√3 - 12√2) / 6

= (8√3 - 15√3 + 18√3 - 3√3 - 12√2) / 6

= (8 - 15 + 18 - 3 - 12)√3 / 6

= (8 - 15 + 18 - 3 - 12)√3 / 6

= -4√3 / 6

= -2√3 / 3

So, the value of the expression 4 tg(30°) - 5 cos(30°) + 6 sin(60°) - 4 cos(45°) - tg(60°) is -2√3 / 3.