Skip to content

Course home

Sign up

Trigonometry and Modelling

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256
Question 21
a.

The identity for sin⁡(A+B)\sin(A + B)sin(A+B) is sin⁡(A+B)=sin⁡Acos⁡B+cos⁡Asin⁡B\sin(A + B) = \sin A \cos B + \cos A \sin Bsin(A+B)=sinAcosB+cosAsinB. Use this identity with B=AB = AB=A to write sin⁡(A+A)\sin(A+A)sin(A+A) in terms of sin⁡A \sin A\,sinA and cos⁡A\cos AcosA.

[1]
b.

Use the identity for sin⁡(A+B)\sin(A + B)sin(A+B) to express sin⁡2A \sin 2A\,sin2A in terms of sin⁡A \sin A\,sinA and cos⁡A\cos AcosA.

[2]
c.

Use the identity for cos⁡(A+B)\cos(A + B)cos(A+B) to express cos⁡2A \cos 2A\,cos2A in terms of sin⁡A \sin A\,sinA and cos⁡A\cos AcosA.

[2]
di.

Hence, express cos⁡2A \cos 2A\,cos2A in terms of cos⁡A\cos AcosA.

[2]
dii.

Hence, express cos⁡2A \cos 2A\,cos2A in terms of sin⁡A\sin AsinA.

[2]
e.

Use the identity for tan⁡(A+B)\tan(A + B)tan(A+B) to express tan⁡2A \tan 2A\,tan2A in terms of tan⁡A\tan AtanA.

[2]
Markscheme

Trigonometry and Modelling Questions

  1. A Level
  2. /Maths
  3. /Trigonometry and Modelling

348 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank