Question

Cos4a+cos2a sin2a=cos2a

Answer 1

Ответ:просто реши в фотомаз

Объяснение:

Answer 2

To solve the equation cos(4a) + cos(2a)sin(2a) = cos(2a), we'll apply trigonometric identities to simplify the equation.

Let's start with the double-angle identity for cosine:

cos(2a) = 2cos²(a) - 1

Substituting this into the equation, we have:

cos(4a) + cos(2a)sin(2a) = 2cos²(a) - 1 + sin(2a)cos(2a)

Now, let's use the identity for the sine of double angle:

sin(2a) = 2sin(a)cos(a)

Substituting this into the equation, we get:

cos(4a) + (2cos²(a) - 1)(2sin(a)cos(a)) = 2cos²(a) - 1 + 2sin(a)cos²(a)

Expanding the terms, we have:

cos(4a) + 4cos²(a)sin(a)cos(a) - 2sin(a)cos²(a) = 2cos²(a) - 1 + 2sin(a)cos²(a)

Rearranging the equation, we have:

cos(4a) + 4cos²(a)sin(a)cos(a) - 2sin(a)cos²(a) - 2cos²(a) + 1 = 0

Combining like terms, we get:

cos(4a) + 2cos²(a)sin(a)cos(a) - 2sin(a)cos²(a) - 2cos²(a) + 1 = 0

Now, let's factor out cos(a) from the second and third terms:

cos(4a) + 2cos²(a)[sin(a) - cos(a)] - 2cos²(a) + 1 = 0

Since we want to find the solutions for a, we can set this equation equal to zero:

cos(4a) + 2cos²(a)[sin(a) - cos(a)] - 2cos²(a) + 1 = 0

This equation can be solved by applying various trigonometric identities and techniques, but it doesn't have a simple algebraic solution. It may require numerical methods or approximations to find the specific values of a that satisfy the equation.