Final answer:
To solve sinx - cosx = 0, we find the angle where sinx equals cosx, which is at 45 degrees or π/4 radians. The product sinx · cosx at this angle is 1/2.
Step-by-step explanation:
The question provided is asking to solve the equation sinx - cosx = 0 for x and then find the value of sinx · cosx. The equation implies that sinx equals cosx, which occurs when x is 45 degrees or π/4 radians since both sine and cosine values are equal for this angle in the first quadrant.
To find the product sinx · cosx, we simply calculate the square of either since sin(45°) = cos(45°). Thus, sin(45°) · cos(45°) = (√2/2) · (√2/2) = 1/2.
However, we should keep in mind that this is only true for the principal angle and that the solution can be generalised to include all angles where sinx = cosx.