Question

2sin^2 2a+2cos((n:2)-a)+2cos^2 2aПри а=n:6

Answer 1

Ответ:

Пошаговое объяснение:

2 1/7 : x = 2 19/28 : 3 3/4

75/28 * x = 15/7 * 15/4

x = 225/28 * 28/75

x = 15/5

x = 3

Проверка: 15/7 : 3 = 75/28 : 15/4

                        5/7 = 75/28 * 4/15  

                        5/7 = 5/7    - верно.

Ответ: {3}

Answer 2

To simplify the expression 2sin^2(2a) + 2cos((n/2)-a) + 2cos^2(2a) when a = n/6, we'll substitute the value of 'a' in the expression and then simplify step by step.

Given: a = n/6

Let's substitute a with n/6:

Expression = 2sin^2(2*(n/6)) + 2cos((n/2)-(n/6)) + 2cos^2(2*(n/6))

Now, simplify each part of the expression:

1. sin^2(2*(n/6)): sin(2x) = 2sin(x)cos(x)

sin^2(2*(n/6)) = (2sin(n/6)cos(n/6))^2 = 4sin^2(n/6)cos^2(n/6)

2. cos((n/2)-(n/6)): Subtracting fractions, we get n/2 - n/6 = 3n/6 - n/6 = 2n/6 = n/3

cos(n/3)

3. cos^2(2*(n/6)): cos^2(2*(n/6)) = (cos(n/3))^2

Now, let's rewrite the expression with the simplified parts:

Expression = 2 * 4sin^2(n/6)cos^2(n/6) + 2cos(n/3) + (cos(n/3))^2

Next, we can combine like terms:

Expression = 8sin^2(n/6)cos^2(n/6) + 2cos(n/3) + (cos(n/3))^2

Finally, the simplified expression is:

8sin^2(n/6)cos^2(n/6) + 2cos(n/3) + (cos(n/3))^2

Please note that this is the simplified form of the expression when a = n/6. If you have a specific value for 'n', you can substitute it in the final expression to get a numerical result.