Question

√3sin870°-2cos(-855°)+ √3ctg930°​

Answer 1

Ответ:решение на фото

Объяснение:

Answer 2

To simplify the expression, let's break it down step by step.

1. First, let's deal with the trigonometric functions:

• sin(870°) is equivalent to sin(870° - 360°) because sine has a period of 360 degrees. So, sin(870°) = sin(510°).

• cos(-855°) is equal to cos(855°) because the cosine function is even, meaning cos(-x) = cos(x).

• ctg(930°) is equivalent to cot(930° - 360°) because cotangent has a period of 360 degrees. So, ctg(930°) = cot(570°).

2. Now, calculate the trigonometric values:

• sin(510°) = sin(510° - 360°) = sin(150°) = √3/2.

• cos(855°) = cos(135°) = -√2/2.

• cot(570°) is the reciprocal of the tangent, so cot(570°) = 1/tan(570°). Since the tangent has a period of 180 degrees, tan(570°) = tan(570° - 180°) = tan(390°). But tan(390°) = tan(390° - 360°) = tan(30°) = 1/√3.

Therefore, cot(570°) = 1/(1/√3) = √3.

3. Now, plug in the calculated values into the original expression:

√3sin870° - 2cos(-855°) + √3ctg930° = √3 * (√3/2) - 2 * (-√2/2) + √3 * √3 = 3/2 + √2 + 3

Finally, the simplified expression is:

√3sin870° - 2cos(-855°) + √3ctg930° = 5/2 + √2.