If , prove that d ( + ) ( + ) + d ( + ) ( + ) + d ( + ) ( + ) = 0, where, ' ' is any…

MATHEMATICS · Subjective · ISC · Mathematics · Sets and Functions · Sets and Functions

Problem

If 2(cos⁡(α−β)+cos⁡(β−γ)+cos⁡(γ−α))+3=02(\cos(\alpha - \beta) + \cos(\beta - \gamma) + \cos(\gamma - \alpha)) + 3 = 0 , prove that dαsin⁡(β+θ)sin⁡(γ+θ)+dβsin⁡(α+θ)sin⁡(γ+θ)+dγsin⁡(α+θ)sin⁡(β+θ)=0,\text{that } \frac{d\alpha}{\sin(\beta + \theta) \sin(\gamma + \theta)} + \frac{d\beta}{\sin(\alpha + \theta) \sin(\gamma + \theta)} + \frac{d\gamma}{\sin(\alpha + \theta) \sin(\beta + \theta)} = 0,where, ' θ\theta ' is any real angle such that α+θ,β+θ,γ+θ\alpha + \theta, \beta + \theta, \gamma + \theta are not the multiple of π\pi .

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