Williamin

To find the angle AA from the equation:

8cos⁡3A+4cos⁡2A−6cos⁡A−1=08cos3A+4cos2A−6cosA−1=0

Steps:

Let x=cos⁡Ax=cosA: 8x3+4x2−6x−1=08x3+4x2−6x−1=0

Approximate solution: Using numerical methods, you find: x≈0.7406x≈0.7406

Calculate angle: A=arccos⁡(0.7406)≈42.22∘A=arccos(0.7406)≈42.22∘ (rounded to two decimal places).