Question

4tg^2 120 +4sin^2 120 -3 cos90 ctg 100

Answer 1

Let's break down the expression step by step:

1. tg^2 120 means "tangent squared of 120 degrees." To calculate this, we first find the tangent of 120 degrees and then square it.

   First, calculate the tangent of 120 degrees: tan(120 degrees) = √3

   Now, square it: (√3)^2 = 3

2. 4sin^2 120 means "four times the sine squared of 120 degrees." To calculate this, we first find the sine of 120 degrees and then square it.

   First, calculate the sine of 120 degrees: sin(120 degrees) = √3/2

   Now, square it: (√3/2)^2 = 3/4

3. -3cos90 means "negative three times the cosine of 90 degrees." To calculate this, we find the cosine of 90 degrees and then multiply it by -3.

   cos(90 degrees) = 0 -3 * 0 = 0

4. ctg 100 means "cotangent of 100 degrees." To calculate this, we find the cotangent of 100 degrees.

   cot(100 degrees) can be calculated as 1/tan(100 degrees).

   First, calculate the tangent of 100 degrees: tan(100 degrees) ≈ -0.17632698

   Now, find the cotangent: cot(100 degrees) ≈ 1 / (-0.17632698) ≈ -5.67232007

Now, let's put it all together:

4tg^2 120 + 4sin^2 120 - 3cos90 ctg 100 = 4(3) + 4(3/4) - 3(0)(-5.67232007) = 12 + 3 - 0 = 15

So, the value of the expression is 15.