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 \phi 1−cosϕ1+1+cosϕ1≡2csc2ϕThe 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} = 8 1−cosϕ1+1+cosϕ1=8find the exact value of cotϕ\cot \phicotϕ.
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
