Question

2sin^2x-2cos2x-sin2x=0

Answer 1

Однородное уравнение 2-ой степени.

Answer 2

To solve the equation 2sin^2x - 2cos2x - sin2x = 0, we can simplify it step by step. Let's break it down:

1. Use the identity sin^2(x) = 1 - cos^2(x) to rewrite sin^2(x): 2(1 - cos^2(x)) - 2cos(2x) - sin(2x) = 0

2. Expand the term -2cos(2x) using the double-angle formula: 2 - 2cos^2(x) - 2(2cos^2(x) - 1) - sin(2x) = 0

3. Simplify the equation further: 2 - 2cos^2(x) - 4cos^2(x) + 2 - sin(2x) = 0 4 - 6cos^2(x) - sin(2x) = 0

4. Use the identity sin(2x) = 2sin(x)cos(x) to rewrite sin(2x): 4 - 6cos^2(x) - 2sin(x)cos(x) = 0

5. Factor out cos(x) from the last two terms: 4 - 6cos^2(x) - 2cos(x)(sin(x) - 3cos(x)) = 0

Now we have two possibilities:

Possibility 1: 4 - 6cos^2(x) - 2cos(x) = 0 Simplifying further: -6cos^2(x) - 2cos(x) + 4 = 0

Possibility 2: sin(x) - 3cos(x) = 0

Please let me know which possibility you would like to explore further.