Final answer:
The expression √(1−cos(6x))/2 can be simplified using the half-angle identity to sin(3x), corresponding to option a).
Step-by-step explanation:
The student's question is asking to simplify the expression √(1−cos(6x))/2. We can apply trigonometric identities to simplify this. Using the half-angle identity, which states that √(1−cos(θ))/2 = sin(θ/2), we identify θ as 6x. Therefore, the expression simplifies to sin(3x).
None of the options provided (sin(3x), cos(3x), tan(3x), cot(3x)) directly correspond to this simplification. However, given that sin(3x) is yielded from the half-angle identity, it would be the closest match to the simplified form of the expression, which corresponds to option a).
To simplify the expression √(1−cos(6x))/2a, we can start by simplifying the numerator. Using the identity sin^2(x) + cos^2(x) = 1, we can rewrite the expression as √(sin^2(6x))/2a.
Taking the square root of sin^2(6x) gives us |sin(6x)|/2a. Since |sin(6x)| and sin(6x) have the same value for all values of x, the final simplified expression is sin(6x)/2a.