Given that cosϕ≠±1\cos \phi \neq \pm 1cosϕ=±1, prove the identity 11−cosϕ+11+cosϕ≡2csc2ϕ\frac{1}{1 - \cos \phi} + \frac{1}{1 + \cos \phi} \equiv 2 \csc^2 \phi1−cosϕ1+1+cosϕ1≡2csc2ϕ
The response RRR of a specific sensor is modeled by the expression R=11−cosϕ+11+cosϕR = \frac{1}{1 - \cos \phi} + \frac{1}{1 + \cos \phi}R=1−cosϕ1+1+cosϕ1. Find the set of values of kkk for which the equation R=kR = kR=k has real solutions for ϕ\phiϕ. Fully justify your answer.
Given that ϕ\phiϕ is in the third quadrant (reflex angle between 180∘180^\circ180∘ and 270∘270^\circ270∘) and 11−cosϕ+11+cosϕ=8\frac{1}{1 - \cos \phi} + \frac{1}{1 + \cos \phi} = 81−cosϕ1+1+cosϕ1=8 find the exact value of cotϕ\cot \phicotϕ.