Answer:
x = arccos(3/4) + 2πn where n = 0,1,2,3,4, ....
Explanation:
We can solve the equation 4cos(x) + 3 = 6 by isolating the cos(x) term on one side of the equation.
4cos(x) + 3 - 3 = 6 - 3
4cos(x) = 3
cos(x) = 3/4
Now we can find the solutions of the equation by finding the values of x that make cos(x) equal to 3/4. Since -π < x < π, we can find the solutions in the range of -π < x < π.
x = cos^-1(3/4) + 2πn, where n is an integer
x = cos^-1(3/4) + 2πn, where n = 0, 1, 2, ...
The solutions are x= cos^-1(3/4) and x = cos^-1(3/4) + 2π, x = cos^-1(3/4) + 4π
Keep in mind that cos^-1(3/4) is the inverse cosine function or arccos(3/4) so the final solution is x = arccos(3/4) + 2πn where n = 0,1,2,3,4, ....