Question

(ctg 30- tg60) - sin 30

Answer 1

$( \cot(30) - \tan(60) ) - \sin(30) = ( \sqrt{3} - \sqrt{3} ) - \frac{1}{2} = 0 - \frac{1}{2} = - \frac{1}{2} = - 0.5$

Answer 2

To calculate the expression (ctg 30 - tg 60) - sin 30, we first need to determine the values of the trigonometric functions involved.

1. cotangent (ctg) 30 degrees: The cotangent of an angle is the reciprocal of its tangent. ctg 30 degrees = 1 / tan 30 degrees

To find tan 30 degrees, we can use the fact that it is the same as sin 30 degrees divided by cos 30 degrees: tan 30 degrees = sin 30 degrees / cos 30 degrees

2. tangent (tg) 60 degrees: tan 60 degrees = sin 60 degrees / cos 60 degrees

3. sine (sin) 30 degrees: This value is well-known: sin 30 degrees = 0.5

4. cosine (cos) 30 degrees and 60 degrees: cos 30 degrees = sqrt(3)/2 cos 60 degrees = 0.5

Now, let's calculate each part step-by-step:

1. ctg 30 degrees = 1 / tan 30 degrees ctg 30 degrees = 1 / (sin 30 degrees / cos 30 degrees) ctg 30 degrees = 1 / (0.5 / (sqrt(3)/2)) ctg 30 degrees = 2 * sqrt(3) / 3

2. tg 60 degrees = sin 60 degrees / cos 60 degrees tg 60 degrees = (sqrt(3)/2) / 0.5 tg 60 degrees = sqrt(3)

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

(ctg 30 - tg 60) - sin 30 = (2 * sqrt(3) / 3 - sqrt(3)) - 0.5

To combine like terms:

= (2 * sqrt(3) / 3 - 3 * sqrt(3) / 3) - 0.5 = (-sqrt(3) / 3) - 0.5 = -sqrt(3)/3 - 3/2

So, the final result is approximately:

(ctg 30 - tg 60) - sin 30 ≈ -1.366