Question

Sin23° - ctg67° * sin67°

Answer 1

!!!!!!!!!!!!!!!!!!!!!!!

Answer 2

1) Применим формулы:
ctgα = cosα/sinα
  и
cos(90°-α) = sinα

sin23° - ctg67° * sin67° =
= sin23° - cos67°/sin67° * sin67° =
= sin23° - cos67° =
= sin23° - cos(90°-23°) =
= sin23° - sin23° = 0

Answer 3

To calculate the expression, we need to use trigonometric identities and convert the trigonometric functions to their respective values.

1. Use the trigonometric identity ctg(θ) = 1 / tan(θ) to convert ctg67° to 1 / tan67°.
2. Use the trigonometric identity tan(θ) = sin(θ) / cos(θ) to convert tan67° to sin67° / cos67°.
3. Use the trigonometric identity cos(θ) = sqrt(1 - sin^2(θ)) to find cos67°.
4. Use the trigonometric identity sin(23°) to find the value of sin23°.

Let's go step by step:

1. ctg67° = 1 / tan67°
2. tan67° = sin67° / cos67°
3. cos67° = sqrt(1 - sin^2(67°))
4. sin23°

I'll now calculate the values and then the final expression:

1. ctg67° = 1 / tan(67°) ≈ 1 / 2.35585 ≈ 0.4254
2. tan67° = sin(67°) / cos(67°) ≈ 0.90334 / 0.42819 ≈ 2.107
3. cos67° = sqrt(1 - sin^2(67°)) ≈ sqrt(1 - 0.90334^2) ≈ sqrt(1 - 0.81507) ≈ sqrt(0.18493) ≈ 0.43049
4. sin23° ≈ 0.39073

Now, let's calculate the final expression:

Sin23° - ctg67° * sin67°

0.39073 - 0.4254 * 0.90334

0.39073 - 0.38425 ≈ 0.00648

So, Sin23° - ctg67° * sin67° ≈ 0.00648.