Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Mathematics
Mathematics
Problem If 2 ( cos ( α − β ) + cos ( β − γ ) + cos ( γ − α ) ) + 3 = 0 2(\cos(\alpha - \beta) + \cos(\beta - \gamma) + \cos(\gamma - \alpha)) + 3 = 0 2 ( cos ( α − β ) + cos ( β − γ ) + cos ( γ − α )) + 3 = 0 that d α sin ( β + θ ) sin ( γ + θ ) + d β sin ( α + θ ) sin ( γ + θ ) + d γ sin ( 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, that sin ( β + θ ) sin ( γ + θ ) d α + sin ( α + θ ) sin ( γ + θ ) d β + sin ( α + θ ) sin ( β + θ ) d γ = 0 , θ \theta θ α + θ , β + θ , γ + θ \alpha + \theta, \beta + \theta, \gamma + \theta α + θ , β + θ , γ + θ π \pi π Browse the problem library