Final answer:
The solution to the equation 2 sin²(x) sin(x) - 1 = 0 would typically require using double-angle identities, but there appears to be a transcription error in the equation. Assuming the corrected equation is 2 sin(x) cos(x) - 1 = 0, the answer would be 45 degrees. However, without the right equation, we can't confidently provide a solution from the options given.
Step-by-step explanation:
To find the solution to the equation 2 sin²(x) sin(x) - 1 = 0, we can use the double-angle identities for sine and cosine. These identities aid in simplifying trigonometric expressions and are essential in solving trigonometric equations. The double-angle formula is sin(2x) = 2sin(x)cos(x). Applying this to the given equation, we recognize that the term 2sin(x)cos(x) can be rewritten as sin(2x), but since there is a sin²(x) instead of a cos(x), it seems there's likely an error in the transcription of the original equation.
Assuming the correct equation is actually 2 sin(x) cos(x) - 1 = 0, which simplifies to sin(2x) = 1, we can solve for x. The value of sin(2x) = 1 occurs when 2x is equal to 90 degrees (or π/2 radians), leading to x = 45 degrees. However, if there is no transcription error and the original equation stands as is, we may need to employ different strategies potentially involving factoring or the quadratic formula to find x.
Without the correct simplification or a correction of the equation, we cannot definitively provide a correct answer from the options given. As for the options provided, we can evaluate each by plugging them into the correct trigonometric identity or equation: (1) 45, (2) 200, (3) 240, (4) 270, (5) 330. For instance, we know that sin(270°) = -1, so substitute x = 270° into the equation does not yield a true statement, and hence is not a solution.