Main 30 · Advanced 12
Consider three points P=(−sin(β−α),−cosβ)P=(-\sin(\beta-\alpha),-\cos\beta)P=(−sin(β−α),−cosβ), Q=(cos(β−α),sinβ)Q=(\cos(\beta-\alpha),\sin\beta)Q=(cos(β−α),sinβ) and R=(cos(β−α+θ),sin(β−θ))R=(\cos(\beta-\alpha+\theta),\sin(\beta-\theta))R=(cos(β−α+θ),sin(β−θ)), where 0<α,β,θ<π40<\alpha,\beta,\theta<\frac\pi40<α,β,θ<4π. Then,
The tangent to the curve y=exy=e^xy=ex drawn at the point (c,ec)(c,e^c)(c,ec) intersects the line joining the points (c−1,ec−1)(c-1,e^{c-1})(c−1,ec−1) and (c+1,ec+1)(c+1,e^{c+1})(c+1,ec+1)