Ответы
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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