To simplify the given trigonometric equation, we can use the product-to-sum identities:
sin A sin B = 0.5[cos(A - B) - cos(A + B)]
Applying this identity to both sides of the equation, we get:
0.5[cos(x - 11x) - cos(x + 11x)] = 0.5[cos(3x - 9x) - cos(3x + 9x)]
Simplifying both sides:
0.5[cos(-10x) - cos(12x)] = 0.5[cos(-6x) - cos(12x)]
cos(-θ) = cos(θ), so we get:
0.5[cos(10x) - cos(12x)] = 0.5[cos(-6x) - cos(12x)]
cos(θ) - cos(φ) = 2 sin(0.5(θ + φ)) sin(0.5(θ - φ)), so:
2 sin(0.5(10x - 12x)) sin(0.5(10x + 12x)) = 2 sin(0.5(-6x - 12x)) sin(0.5(-6x + 12x))
sin(-θ) = -sin(θ), so by simplifying further, we get:
2 sin(-x) sin(11x) = 2 sin(-9x) sin(3x)
-2 sin(x) sin(11x) = -2 sin(9x) sin(3x)
sin(x) sin(11x) = sin(9x) sin(3x)
Therefore, the simplified form of the given trigonometric equation is sin(x) sin(11x) = sin(9x) sin(3x).
To simplify the given trigonometric equation, we can use the product-to-sum identities:
sin A sin B = 0.5[cos(A - B) - cos(A + B)]
Applying this identity to both sides of the equation, we get:
0.5[cos(x - 11x) - cos(x + 11x)] = 0.5[cos(3x - 9x) - cos(3x + 9x)]
Simplifying both sides:
0.5[cos(-10x) - cos(12x)] = 0.5[cos(-6x) - cos(12x)]
cos(-θ) = cos(θ), so we get:
0.5[cos(10x) - cos(12x)] = 0.5[cos(-6x) - cos(12x)]
cos(θ) - cos(φ) = 2 sin(0.5(θ + φ)) sin(0.5(θ - φ)), so:
2 sin(0.5(10x - 12x)) sin(0.5(10x + 12x)) = 2 sin(0.5(-6x - 12x)) sin(0.5(-6x + 12x))
sin(-θ) = -sin(θ), so by simplifying further, we get:
2 sin(-x) sin(11x) = 2 sin(-9x) sin(3x)
-2 sin(x) sin(11x) = -2 sin(9x) sin(3x)
sin(x) sin(11x) = sin(9x) sin(3x)
Therefore, the simplified form of the given trigonometric equation is sin(x) sin(11x) = sin(9x) sin(3x).