Question

Sin 4x = 2cos² x - 1

Answer 1

Ответ:

Объяснение:

Решение на фотке))

Answer 2

Ответ:=======

Объяснение:во вложении

Answer 3

To solve the equation sin(4x) = 2cos²(x) - 1, we can use trigonometric identities to simplify the equation and find the values of x that satisfy it.

Let's start by using the double angle identity for sine:

sin(2θ) = 2sin(θ)cos(θ)

Substitute θ = 2x:

sin(4x) = 2sin(2x)cos(2x)

Now, let's use the Pythagorean identity for sine and cosine:

sin²(θ) + cos²(θ) = 1

Substitute θ = x:

sin²(x) + cos²(x) = 1

Rearrange the equation to solve for sin²(x):

sin²(x) = 1 - cos²(x)

Now we can substitute this into the equation for sin(4x):

2sin(2x)cos(2x) = 2(1 - cos²(x))cos(2x)

Now, use the double angle identity for cosine:

cos(2θ) = 2cos²(θ) - 1

Substitute θ = x:

cos(2x) = 2cos²(x) - 1

Now, substitute this back into the equation for sin(4x):

2sin(2x)cos(2x) = 2(1 - cos²(x))cos(2x)

2sin(2x)cos(2x) = 2cos(2x) - 2cos²(x)

Divide both sides of the equation by 2cos(2x) to simplify:

sin(2x) = 1 - cos(x)

Now we have a trigonometric equation involving sin and cos. However, solving this equation directly can be quite complex due to the presence of trigonometric functions of different angles. Depending on the specific requirements, you might need to use numerical methods or approximations to find the values of x that satisfy this equation.