Skip to content

Course home

1.8.8 Proofs with trigonometric identities

1.8.8 Proofs with trigonometric identities

EasyMediumHard
123456789101112131415161718192021222324252627282930
Question 11
i.

Show that

cot⁡θ−tan⁡θcot⁡θ+tan⁡θ≡cos⁡2θ \frac{\cot \theta - \tan \theta}{\cot \theta + \tan \theta} \equiv \cos 2\theta cotθ+tanθcotθ−tanθ​≡cos2θ

for θ≠nπ2\theta \neq \frac{n\pi}{2}θ=2nπ​ where n∈Zn \in \mathbb{Z}n∈Z.

[3]
ii.

The power output PPP (in Watts) of a specific AC circuit component is modelled by the function P(t)=11cos⁡2(2t−40∘)P(t) = 11 \cos^2(2t - 40^\circ)P(t)=11cos2(2t−40∘), where ttt is a phase angle measured in degrees and 0∘≤t<90∘0^\circ \le t < 90^\circ0∘≤t<90∘.

Determine the values of ttt for which the power output is exactly 333 Watts, giving your answers to one decimal place. (Solutions based entirely on graphical or numerical methods are not acceptable.)

[5]
Markscheme

1.8.8 Proofs with trigonometric identities Questions

  1. A Level
  2. /Maths
  3. /1.8.8 Proofs with trigonometric identities

38 exam-style questions on AQA A Level Maths 1.8.8 Proofs with trigonometric identities. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank