Final answer:
The original equation provided by the student is incorrect as it misuses the double angle identity for sine. The formula sin(20) does not equate to 2 sin(0) cos(0) because the angle in sin and cos must be the same and non-zero for the identity to hold true.
Step-by-step explanation:
The student appears to be confused about the proper application of trigonometric identities and specific values. The goal is to show that sin(2°) = 2 sin(°) cos(°) which is a condensed form of the double angle formula for sine. However, this identity is only valid if the angle in sin and cos is the same, which is not the case when the angle is 0. Also, the provided equation is inconsistent with known trigonometric identities, because sin(20) does not equal 2 sin(0) cos(0). Instead, the correct double angle identity should be sin(2θ) = 2 sin(θ) cos(θ), where θ is the same angle for both sine and cosine.
To correct the statement and apply it to a 20-degree angle, you would use sin(2× 10°) = 2 sin(10°) cos(10°). Here, θ=10°, and you're applying the correct double angle formula for sine. The original statement sin(20) = 2 sin(0) cos(0) is false because sin(0) = 0, which would make the right-hand side of the equation zero.