Question

Sin x cos x- cos2x=0

Answer 1

Ответ:

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Answer 2

To solve the equation sin(x)cos(x) - cos(2x) = 0, we can use trigonometric identities to simplify it. Let's start by manipulating the equation:

sin(x)cos(x) - cos(2x) = 0

Using the identity cos(2x) = 1 - 2sin^2(x), we can substitute it into the equation:

sin(x)cos(x) - (1 - 2sin^2(x)) = 0

Expanding the equation:

sin(x)cos(x) - 1 + 2sin^2(x) = 0

Rearranging the terms:

2sin^2(x) + sin(x)cos(x) - 1 = 0

Now, let's factor the equation:

(2sin(x) - 1)(sin(x) + 1) = 0

Setting each factor to zero:

2sin(x) - 1 = 0 or sin(x) + 1 = 0

For the first factor, 2sin(x) - 1 = 0, we solve for sin(x):

2sin(x) = 1 sin(x) = 1/2

This gives us the solutions: x = π/6 + 2πn, where n is an integer.

For the second factor, sin(x) + 1 = 0, we solve for sin(x):

sin(x) = -1

This gives us the solution: x = (2n + 1)π, where n is an integer.

Therefore, the solutions to the equation sin(x)cos(x) - cos(2x) = 0 are:

x = π/6 + 2πn, where n is an integer, x = (2n + 1)π, where n is an integer.