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Given that (a−b)sin(θ+ϕ) = (a+b)sin(θ−ϕ) and a tan(θ/2) − b tan(ϕ/2) = c, which of the following holds true?

1. b tan(ϕ) = a tan(θ)
2. a tan(ϕ) = b tan(θ)
3. sin(ϕ) = −2bc/(a²−b²−c²)
4. sin(θ) = −2ac/(a²−b²+c²)

Correct answer: sin(ϕ) = −2bc/(a²−b²−c²)

Solution

The correct relationship is sin(ϕ) = −2bc/(a²−b²−c²), which can be determined by analyzing the given equations and applying trigonometric identities.

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