Question

Tg^2 * 2p/3 - ctg^2 * 2p/3 - 10/3 * sin^2*2p/3 + cos^2*2p/3

Answer 1

Ответ:

Я так решила

Объяснение:

tg(2п/3)•sin(3п/2) + 3•ctg(п/3) - 2•cos(п/4) = tg( п - п/3 )•sin( п + п/2 ) + 3•сtg(п/3) - 2•cos(п/4) = - tg(п/3)•( - sin(п/2) ) + 3•ctg(п/3) - 2•cos(п/4) = - √3•( - 1 ) + 3•( √3/3 ) - 2•( √2/2 ) = √3 + √3 - √2 = 2√3 - √2

ОТВЕТ: 2√3 - √2

Answer 2

It seems like you have a mathematical expression involving trigonometric functions. Let's break it down step by step and simplify it:

1. Tg^2(2π/3) is the square of the tangent function with an angle of 2π/3.
2. Ctg^2(2π/3) is the square of the cotangent function with an angle of 2π/3.
3. Sin^2(2π/3) is the square of the sine function with an angle of 2π/3.
4. Cos^2(2π/3) is the square of the cosine function with an angle of 2π/3.

Now, let's calculate each of these trigonometric values:

1. Tan(2π/3) is equal to √3, so Tan^2(2π/3) = (√3)^2 = 3.
2. Cot(2π/3) is equal to 1/√3, so Cot^2(2π/3) = (1/√3)^2 = 1/3.
3. Sin(2π/3) is equal to √3/2, so Sin^2(2π/3) = (√3/2)^2 = 3/4.
4. Cos(2π/3) is equal to -1/2, so Cos^2(2π/3) = (-1/2)^2 = 1/4.

Now, we can substitute these values back into the original expression:

3 * 2/3 - 1/3 * 10/3 - 3/4 * 3 + 1/4

Now, let's simplify it further:

2 - 10/9 - 9/4 + 1/4

Now, find a common denominator for the fractions:

(8/4) - (10/9) - (18/4) + (1/4)

Now, add and subtract the fractions:

(8/4 - 18/4) - (10/9 - 1/4)

-10/4 - (10/9 - 1/4)

Now, subtract the fractions:

-5/2 - (10/9 - 1/4)

To subtract these fractions, find a common denominator, which is 36:

-5/2 - (40/36 - 9/36)

Now, subtract the fractions:

-5/2 - 31/36

To combine the fractions, find a common denominator, which is 36:

(-90/36) - (31/36)

Now, subtract the fractions:

-90/36 - 31/36 = -121/36

So, the simplified expression is:

-121/36