Sin 6a-sin4a+sina/cos6a+cos4a+cosa

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This expression can be simplified by using trigonometric identities. First, we can simplify cos6a + cos4a + cosa using the sum-to-product formula:

cos6a + cos4a + cosa = 2cos(5a)cos(a) + cos(a) = 2cos(5a)cos(a) + cos(0)cos(a) = 2cos(5a)cos(a) + cos(5a)cos(a) = 3cos(5a)cos(a)

Now, the expression becomes:

sin(6a) - sin(4a) + sin(a) / (3cos(5a)*cos(a))

Next, we simplify the numerator using the sum-to-product formula for sine:

sin(6a) - sin(4a) + sin(a) = 2sin(3a)cos(3a) - 2sin(2a)cos(2a) + sin(a) = 2sin(3a)(1 - 2sin^2(a)) - 2(2sin(a)cos(a)) + sin(a) = 2sin(3a) - 4sin(3a)sin^2(a) - 4sin(a)cos(a) + sin(a) = sin(3a)(2 - 4sin^2(a)) - 4sin(a)cos(a) + sin(a) = sin(3a)(2cos^2(a)) - 4sin(a)cos(a) + sin(a) = 2sin(3a)cos^2(a) - 4sin(a)cos(a) + sin(a) = sin(a)(2cos^2(5a) - 4cos(5a) + 1)

Substitute this back into the expression:

sin(a)(2cos^2(5a) - 4cos(5a) + 1) / (3cos(5a)*cos(a))

Simplify further if needed.