Given cos(75∘)=6−24\displaystyle \cos (75^\circ) = \frac{\sqrt{6} - \sqrt{2}}{4}cos(75∘)=46−2 and sin(75∘)=6+24\displaystyle \sin (75^\circ) = \frac{\sqrt{6} + \sqrt{2}}{4}sin(75∘)=46+2
Show that tan2(75∘)\tan^2 (75^\circ)tan2(75∘) can be written in the form a+b3a + b\sqrt{3}a+b3
Fully justify your answer.
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
