SPS SPS FM 2020 June — Question 4 4 marks

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2020
SessionJune
Marks4
TopicAddition & Double Angle Formulae
TypeDerive triple angle formula only
DifficultyModerate -0.5 This is a straightforward derivation using the addition formula for tan(A+B) with A=2θ and B=θ. It requires applying the double angle formula for tan 2θ, then substituting into tan(A+B) and simplifying algebraically. While it involves multiple steps and careful algebra, it's a standard textbook exercise with a clear method and no novel insight required—slightly easier than average.
Spec1.05l Double angle formulae: and compound angle formulae

4. Use the identity for \(\tan ( A + B )\) to show that $$\tan 3 \theta \equiv \frac { 3 \tan \theta - \tan ^ { 3 } \theta } { 1 - 3 \tan ^ { 2 } \theta }$$

4.

Use the identity for $\tan ( A + B )$ to show that

$$\tan 3 \theta \equiv \frac { 3 \tan \theta - \tan ^ { 3 } \theta } { 1 - 3 \tan ^ { 2 } \theta }$$

\hfill \mbox{\textit{SPS SPS FM 2020 Q4 [4]}}