Sin(п/2+х)-cos (п+х)+1=0

Предыдущий
вопрос Следующий
вопрос

To solve this trigonometric equation, we can use the trigonometric identities for sine and cosine.

First, let's simplify the given equation by replacing п with pi (π) for clarity:

sin(π/2 + x) - cos(π + x) + 1 = 0

Using the sum and difference identities for sine and cosine, we can rewrite the equation:

sin(π/2)cos(x) + cos(π/2)sin(x) - cos(π)cos(x) + sin(π)sin(x) + 1 = 0

Now we can substitute the trigonometric values:

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

From the unit circle or reference angles, we know that the cosine function is equal to -1/2 at π/3 and 5π/3 (or π ± π/3). Therefore, the solutions for x are:

x = π/3 + 2πn = 2π/3 + 2πn, where n is an integer.