Skip to content

Course home

Sign up

1.8 E: Trigonometry

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169
Question 158
i.

Show that

1tan⁡θ−tan⁡θ≡cos⁡2θsin⁡θcos⁡θ \frac{1}{\tan \theta} - \tan \theta \equiv \frac{\cos 2\theta}{\sin \theta \cos \theta} tanθ1​−tanθ≡sinθcosθcos2θ​

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

[3]
ii.

Solve, for 0∘≤x<90∘0^\circ \le x < 90^\circ0∘≤x<90∘, the equation

5sin⁡2(2x−15∘)=2 5 \sin^2(2x - 15^\circ) = 2 5sin2(2x−15∘)=2

giving your answers in degrees to one decimal place. (Solutions based entirely on graphical or numerical methods are not acceptable.)

[6]
Markscheme

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, 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. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank