CAIE A-Level Mathematics 2.3.2 Trig identities

CAIE A-Level Mathematics 2.3.2 Trig identities
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise choosing trig identities to simplify expressions, prove results and solve equations within stated angle intervals.

How this is tested

  • transform equations into one trig function before solving quadratics in sin, cos or tan
  • rewrite a sin x + b cos x as R sin(x ± α), then use it to solve within a given interval
  • prove identities by selecting double-angle, reciprocal or Pythagorean forms and simplifying cleanly

Question 4

[Maximum number: 5]

Solve the equation cot⁡θtan⁡(θ+45∘)=7\cot \theta \tan \left(\theta+45^{\circ}\right)=7 for 0∘<θ<90∘0^{\circ}<\theta<90^{\circ}.