Cosx+cos5x+2sin*2x=1

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To solve this equation, we need to use trigonometric identities to simplify the equation.

First, we can rewrite 2sin^2(x) as 1 - cos^2(x) using the Pythagorean identity for sine and cosine.

The equation becomes:

cos(x) + cos(5x) + 1 - cos^2(2x) = 1

Next, we can use the double-angle identity for cosine to simplify cos^2(2x):

cos^2(2x) = (1 + cos(4x)) / 2

Substitute this into the equation:

cos(x) + cos(5x) + 1 - (1 + cos(4x))/2 = 1

Simplify further:

cos(x) + cos(5x) + 1 - 1/2 - cos(4x)/2 = 1

cos(x) + cos(5x) - cos(4x)/2 = 1/2

At this point, it may be difficult to simplify further without additional context or instructions. The equation may need to be approached in a different manner depending on what the desired outcome is.