Question

8cos2x +6sinx-3=0 помогите

Answer 1

Відповідь:To solve the equation 8cos(2x) + 6sin(x) - 3 = 0, we can use trigonometric identities to simplify it.

First, let's use the double-angle identity for cosine, which states that cos(2x) = 2cos^2(x) - 1. Replacing cos(2x) with this expression, the equation becomes:

8(2cos^2(x) - 1) + 6sin(x) - 3 = 0

Rearranging the equation, we have:

16cos^2(x) + 6sin(x) - 11 = 0

Now, let's use another trigonometric identity, sin^2(x) + cos^2(x) = 1, to replace cos^2(x) with (1 - sin^2(x)):

16(1 - sin^2(x)) + 6sin(x) - 11 = 0

Simplifying further:

16 - 16sin^2(x) + 6sin(x) - 11 = 0

Rearranging and combining like terms:

-16sin^2(x) + 6sin(x) + 5 = 0

Now, we can solve this quadratic equation for sin(x) using factoring, completing the square, or the quadratic formula. Unfortunately, the given equation does not have a simple solution, and its roots are not readily obtainable with elementary methods. You may need to use numerical methods or approximation techniques to find the solutions.

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