Cos(x+п/3)cos(x-п/3)-0.25=0

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To solve the given equation cos(x+π/3)cos(x-π/3) - 0.25 = 0, we can use the trigonometric identity:

cos(A)cos(B) = 0.5[cos(A + B) + cos(A - B)]

Applying this identity to the given equation, we get:

0.5[cos(2x) + cos(-π/3)] - 0.25 = 0
0.5[cos(2x) + cos(π/3)] - 0.25 = 0
0.5[cos(2x) + 0.5] - 0.25 = 0
0.25cos(2x) + 0.25 - 0.25 = 0
0.25cos(2x) = 0

Dividing both sides by 0.25, we get:

cos(2x) = 0

This implies that 2x = π/2 or 2x = 3π/2.

Therefore, the solutions for x are:

x = π/4, 3π/4