Question

Cos(6π​+α)×cos(6π​−α)​

Answer 1

Ответ: Cos(6п+а)Cos(6п-а)=2Cos6пCosa

Объяснение:

Answer 2

To simplify the expression cos(6π + α) × cos(6π - α), we can use the cosine double-angle identity:

cos(2θ) = 2cos²(θ) - 1

Let's substitute θ with (6π + α) and (6π - α):

cos(2(6π + α)) = 2cos²(6π + α) - 1

cos(2(6π - α)) = 2cos²(6π - α) - 1

Simplifying the expressions further:

cos(12π + 2α) = 2cos²(6π + α) - 1

cos(12π - 2α) = 2cos²(6π - α) - 1

Since cos(12π) = 1 (cosine of any multiple of 2π is 1), we can simplify the expressions again:

cos(2α) = 2cos²(6π + α) - 1

cos(-2α) = 2cos²(6π - α) - 1

Using the identity cos(-θ) = cos(θ), we can rewrite the second expression as:

cos(2α) = 2cos²(6π - α) - 1

Now we have two equations:

cos(2α) = 2cos²(6π + α) - 1

cos(2α) = 2cos²(6π - α) - 1

Since the left sides of both equations are equal, we can equate the right sides:

2cos²(6π + α) - 1 = 2cos²(6π - α) - 1

Now we can cancel out the common terms:

2cos²(6π + α) = 2cos²(6π - α)

Dividing both sides by 2:

cos²(6π + α) = cos²(6π - α)

Taking the square root of both sides (assuming we are dealing with real numbers):

cos(6π + α) = ±cos(6π - α)

So, cos(6π + α) × cos(6π - α) can be either cos(6π + α) × cos(6π - α) = cos²(6π - α) or cos(6π + α) × cos(6π - α) = -cos²(6π - α), depending on the value of α.