Let's first simplify the given equation by using the trigonometric identity sin^2(x) = 1/2 - 1/2cos(2x):
3(1/2 - 1/2cos(6x)) - 5sin(6x) + 1 = 03/2 - 3/2cos(6x) - 5sin(6x) + 1 = 05/2 - 3/2cos(6x) - 5sin(6x) = 03/2cos(6x) + 5sin(6x) = 5/2
Now, we can use the cosine sum formula to rewrite the left side of the equation:
3/2(cos(6x)cos(0) - sin(6x)sin(0)) + 5sin(6x) = 5/23/2(cos(6x)1 - sin(6x)0) + 5sin(6x) = 5/23/2cos(6x) + 5sin(6x) = 5/2
Therefore, the given equation simplifies to 3/2cos(6x) + 5sin(6x) = 5/2.
Let's first simplify the given equation by using the trigonometric identity sin^2(x) = 1/2 - 1/2cos(2x):
3(1/2 - 1/2cos(6x)) - 5sin(6x) + 1 = 0
3/2 - 3/2cos(6x) - 5sin(6x) + 1 = 0
5/2 - 3/2cos(6x) - 5sin(6x) = 0
3/2cos(6x) + 5sin(6x) = 5/2
Now, we can use the cosine sum formula to rewrite the left side of the equation:
3/2(cos(6x)cos(0) - sin(6x)sin(0)) + 5sin(6x) = 5/2
3/2(cos(6x)1 - sin(6x)0) + 5sin(6x) = 5/2
3/2cos(6x) + 5sin(6x) = 5/2
Therefore, the given equation simplifies to 3/2cos(6x) + 5sin(6x) = 5/2.