(1-cosx)(4+3cos2x)=0

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To solve this equation, you first need to distribute the terms:

(1 - cosx)(4 + 3cos2x) = 4 + 3cos2x - 4cosx - 3cosx*cos2x

Next, we can simplify the equation further by using the double angle identity cos2x = 2cos^2(x) - 1:

(1 - cosx)(4 + 3(2cos^2(x) - 1) - 4cosx - 3cosx(2cos^2(x) - 1)

Now, distribute and simplify the terms:

4 + 6cos^2(x) - 3 - 8cosx - 3cosx(2cos^2(x) - 1)

4 + 6cos^2(x) - 3 - 8cosx - 6cos^3(x) + 3cosx

Finally, combine like terms and set the equation equal to 0 to solve for the values of x:

6cos^2(x) - 6cos^3(x) - 5cosx + 1 = 0

However, this is a more complex trigonometric equation that may not have a simple algebraic solution. You may need to use numerical methods or a graphing calculator to find the values of x that satisfy this equation.