CAIE A-Level Mathematics 1.5.4 Trig identities

Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise proving identities, simplifying trig expressions and rewriting equations using sin, cos, tan and Pythagorean identities.

How this is tested

prove identities by expanding brackets and replacing sin^2 x + cos^2 x with 1
rewrite equations using tan θ = sin θ/cos θ before forming a quadratic in sin θ or cos θ

[Maximum number: 4]

Show that $\cos 4 x+2 \sin ^{2} x-1 \equiv 8 \sin ^{4} x-6 \sin ^{2} x$ .