Question

С1. 10cosx-10sinx+sin2x-cos2x=1 [ -7pi/6; pi/2]

Answer 1

   А задание написать?

Answer 2

To solve the equation C1: 10cos(x) - 10sin(x) + sin(2x) - cos(2x) = 1 in the interval [-7π/6, π/2], we'll first simplify the equation and then find the solutions.

Let's simplify the equation step by step:

1. Use the trigonometric identities:

   • sin(2x) = 2sin(x)cos(x)
   • cos(2x) = cos^2(x) - sin^2(x)

   The equation becomes: 10cos(x) - 10sin(x) + 2sin(x)cos(x) - (cos^2(x) - sin^2(x)) = 1

2. Rearrange the equation and combine like terms: -cos^2(x) + 10cos(x) - sin^2(x) + 2sin(x)cos(x) - 10sin(x) = 1

3. Combine the terms with cos(x) and sin(x): -(cos^2(x) + sin^2(x)) + 10cos(x) + 2sin(x)cos(x) - 10sin(x) = 1

   Recall that cos^2(x) + sin^2(x) = 1: -1 + 10cos(x) + 2sin(x)cos(x) - 10sin(x) = 1

4. Simplify further: 10cos(x) + 2sin(x)cos(x) - 10sin(x) = 2

Now, we can solve this simplified equation in the given interval [-7π/6, π/2]. Unfortunately, this equation does not have a simple algebraic solution. We'll need to use numerical methods or approximation techniques to find the solutions.

One common method is to use a numerical solver or a graphing calculator to approximate the solutions. Using such a tool, you can plot the graph of the equation and find the x-values where it intersects the line y = 1 in the given interval.