Cos x cos5x= cos6x

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To solve the equation cos x cos 5x = cos 6x, we can use the trigonometric identity:

cos(a) cos(b) = 0.5 [cos(a + b) + cos(a - b)]

Applying this identity to the left side of the equation:

cos x cos 5x = 0.5 [cos(x + 5x) + cos(x - 5x)]
cos x cos 5x = 0.5 [cos(6x) + cos(-4x)]
cos x cos 5x = 0.5 [cos(6x) + cos(4x)]

Therefore, the equation simplifies to:

0.5 [cos(6x) + cos(4x)] = cos(6x)

Multiplying both sides by 2:

cos(6x) + cos(4x) = 2cos(6x)

Rearranging terms:

cos(4x) = cos(6x) - cos(6x)
cos(4x) = 0

Hence, the solution to the equation cos x cos 5x = cos 6x is cos 4x = 0.