cos^2(x)(1+6cos(x)) = 1cos^2(x) + 6cos^3(x) = 1cos^2(x) = 1 - 6cos^3(x)
Substitute cos^2(x) = 1 - sin^2(x):
1 - sin^2(x) = 1 - 6cos^3(x)sin^2(x) = 6cos^3(x)
Then we know that sin^2(x) = 1 - cos^2(x), so we can substitute the equation:
1 - cos^2(x) = 6cos^3(x)cos^2(x) + 6cos^3(x) - 1 = 0
This is a cubic equation in terms of cos(x), and can be solved using various methods such as synthetic division or numerical methods.
cos^2(x)(1+6cos(x)) = 1
cos^2(x) + 6cos^3(x) = 1
cos^2(x) = 1 - 6cos^3(x)
Substitute cos^2(x) = 1 - sin^2(x):
1 - sin^2(x) = 1 - 6cos^3(x)
sin^2(x) = 6cos^3(x)
Then we know that sin^2(x) = 1 - cos^2(x), so we can substitute the equation:
1 - cos^2(x) = 6cos^3(x)
cos^2(x) + 6cos^3(x) - 1 = 0
This is a cubic equation in terms of cos(x), and can be solved using various methods such as synthetic division or numerical methods.