Prove that for real \(\theta\),
\[\cos(5\theta) = 16 \cos^5 \theta - 20 \cos^3 \theta + 5 \cos \theta\]
and
\[\sin(5\theta) = 5 \cos^4 \theta \sin \theta - 10 \cos^2 \theta \sin^3 \theta + \sin^5 \theta.\]
Hence express \(\tan (5 \theta)\) in terms of \(\tan \theta\).

\[\cos(5\theta) = 16 \cos^5 \theta - 20 \cos^3 \theta + 5 \cos \theta\]

\[\sin(5\theta) = 5 \cos^4 \theta \sin \theta - 10 \cos^2 \theta \sin^3 \theta + \sin^5 \theta.\]

Hence express \(\tan (5 \theta)\) in terms of \(\tan \theta\).

Proving Trigonometric Ratios by Complex Numbers [Out of Syllabus]

Complex Numbers

International Baccalaureate Higher Level Mathematics

Example for calculating multiple angle formulae

Example for calculating multiple angle formulae